The fact that the tenant does not want to pay for the repair now would lead me to not extend the lease.  

Why doesn't that logic extend to maintenance dollars budgeted from the rental revenue?

The question I have is, "How many times can an average Joe do this until the bank lenders consider them over extended?"

But if you have done something negligent that harms your tenants your screwed LLC, Partnership or held personally, negligence is negligence and they will get you if they have a good lawyer.I personally own some houses in an LLP and some personally, I just have very large Liability coverage and an Umbrella policy that extends to my rentals as well.Disclaimer I am not a lawyer or an accountant... just sharing conversations I have had with people claiming to be lawyers and accountants. 

And the seller knows he won’t be stuck with a low interest loan if it extends out.

Additionally, closing was extended by nearly 2 months despite being just a step away the whole time (more on that below) There's more to an appraisal than the dollar value: when I got my first appraisal back for $160k, I was ecstatic.

We had disclosed that we had water in the basement, but cleaned and extended the gutters (they were dumping the rain water right next to the house) and hadn't had any issues since.

I am not an attorney and am not familiar with your state laws so rather than getting opinions here, I suggest you go right to the source and ask an attorney or licensed professional locally who would know the answer to this.It appears on the surface like you gave all the legal notice and had an agreement to extend the lease for one year, now it is the tenant who wants to change it.

Most people will go through a traditional mortgage loan, one extended by a standard financial provider such as a bank.

Don't over-extend yourself to make the deal work.