Should I ask for a reduction of offer after bad roof inspection?

I would ask them to split the cost of a new roof and ask them to split the cost for a 3 year roof certification, so that you can get insurance on the house at a reasonable cost for that amount of time. A roof certification will give you piece of mind and will give you time to save your half for new roof.

The owners may refuse, but you need to tell them that you want the house, but that it is a big expense for you that you cannot pay alone. If you have a good agent, I think that they can help you make the case for a split. Even getting a credit for 40% of the cost would go a along way to the new roof and it is likely that you can shop the bids to get it done for less depending on the size of the house.

Simply put.....it doesn't hurt to ask.  Your initial offer was based on what was told to you.  Now you have done investigations that prove otherwise.  So ask.  They can either say yes or no or come up with a compromise.  Then you can decide if you are comfortable with their answer or walk away (if you are still in your investigation period).  Good luck!

OtterRock,
Thanks for your response.   
I can't believe I am asking for advise on Zillow either, however I am just receiving conflicting advice from others.  Those close to me say  that I should ask for a new roof/or money.  My realtor is saying that I have no real basis for getting money back, and that it is wishful thinking.   Now I have no reason to think she is trying to screw me [she has been great so far], but I am aware of the fact that she wants to get this done ASAP.  She did say she will do whatever I wish, but I just want to get an outsiders opinion so I can stand firm on a subject I know little about if she tries to change my mind.  I want her to fight, not cave in and say I am crazy to the sellers agent. 

I am amazed you are asking Zillow for home buying advise. Being your first home, you Yes, you would ask for the seller to take less, or to fix the problem with the roof BEFORE closing on the sale. If the owner refuses to make the repairs, or to offer you enough off the price of the home to make the repairs yourself, you should walk away and find a home with less issues and a seller who will work with you. Your contract should have included a walk away clause if the home failed the inspection. It did, the roof was not as they stated. Walk away.
Real estate agents are not always going to be honest with you, especially if they are working for the seller ... I know they will not like me to say that, but it is generally true. They will tell you whatever it takes to get a sale, get their commission. Being your first home, you should find someone you trust with home buying experience, and take their advise, as they have nothing to gain by answering your question. I am a stranger, but have bought many homes and sold many homes, and only on a couple occasions did I allow a real estate agent, also know as a middleman with their hand out for money they in no way earn... I have bought and sold several homes without an agent, you should look into homes for sale by owner. they and the title company can walk you through the easy to understand process. Agents want you to think it is impossible to buy a home without their help. Somehow, Americans bought and sold property themselves for thousands of years before someone got in the middle and made it look very complicated. It is not. how hard do you have to work to make thousands of dollars, even tens of thousands of dollars. Well, having real estate agents in my family, I know for a fact they shower in the morning to look pretty, not in the evening because they worked so hard all day... they are part of the reason our economy crashed, as the greed factor with agents, brokers and the banks was not missed by real estate agents. They made vast amounts on all the overpriced homes they helped rip people off with... on most deals, the agent sets the price, or at least steers you towards what they feel the home should be worth. A home is only worth what someone is willing to pay for it. The problem was also greedy people who also were buying more house than they could afford and they knew it. But the agents, etc. do not care if you wind up in bankruptcy and foreclosure, they will swoop right in and offer to sell the home again... making more unearned money. Roof issues are a deal breaker, and with all the homes available, you should keep looking or make the seller fix the roof if they want you to purchase it. YOU have the power, you are the guy with the money.  Happened to my family. Don't give your money away, make the agent find you a house without any problems, then make the seller pay part of your closing costs. If you are  veteran, know your rights and make sure you are given 3% of the sale price towards your closing costs... and vets do not pay 'points' either... Everything is negotiable in a home sale, you have the upper hand, as you are the buyer in a buyers market. Hope this helped, I know it was long... no spam here, no self promotion, just honesty that I did not get when I bought my first home. Even the commission an agent gets is negotiable, when did we let them go from earning 3% on a sale to 7%? I told the last agent I was involved with who was selling my dad's home that if she wanted the listing, she would have to take a smaller commission. She did and she got 5% on the sale. A fair amount, except they did none of the work that went into getting it ready to sell... 
I wish you luck, there are people out there just trying to get your money for nothing, be wise and do not jump into signing anything until you have found the perfect home. Don't let anyone hurry you into any decisions, that only works well for the sellers and agents, never the buyer.
Happy home buying, be wise, beware and be informed of your rights as a buyer! 
It sounds like you can walk away, the house did not pass inspection. If you can, do. There are sooo many homes for sale and the values will not be going up any time soon!
My opinions and facts as of my experience... just trying to help a buyer in a sea of people looking to make money off of you. Good luck.

Darrell,
Thanks for your answer.  Our insurance company said they would insure the roof, BUT did take note of its age and wear.  He told me specifically "If you don't replace it within 5 years we will have to increase your payments".

So basically the roof has a ticking clock on it independent of how it actually holds up.  It has to come down soon. 

And we are not paying cash... I wish though.

If you are getting a mortgage and the appraiser makes a note or your insurance company states the roof if uninsurable the seller will have to replace the roof unless they are selling to a cash buyer that asks for a price reduction due to the roof condition.

I would request a repair credit for perhaps half of the cost of the roof with 30 year shingles.  Then, when it is time to replace it you can determine if you wish to pay the extra for 50 year shingles or another type of roof covering.