The reduction of 6250 would put my final purchase price to 51,250.  

If you sell a rental with a mortgage or other secured loan, you'll have to purchase your replacement property with a mortgage or pay tax on the reduction in liability. 

A recession won't completely kill short-term rentals but will reduce the number of clients and the nightly rate until a recovery starts again.Assuming that your STR has sufficient margins to price aggressively so that occupancy can be kept up, there isn't that much to worry about other than a temporary reduction in cash flow.

Renovations and repairs would be physical improvements.Rent increase or expense reduction would be financial improvements.You can do either or both.

So they got a $100/month reduction for 4 months?

If they want to test the market have in the listing agreement where " You will try their price for 2 weeks and then there are automatic price reductions built in to the listing agreement ".This way you are not begging for a reduction.

Don't hire contractors, who show up in a pressed shirt, can speak both Spanish and English and do zero work but pocket a fat margin.  

Generally, cases in which an arms-length sale transaction sets the value are slam-dunk cases, but they will almost never grant a reduction without a sale (you have to appeal by phone).

All of those things have tangible (but hard to quantify) value but if you're sitting in San Diego, Colorado, Michigan, etc. that tangible value drops to a big ol' fat zero. 

Even at significant price reductions, people usually still can't afford cash purchases.