The rest (and the depreciation recapture) indefinitely deferred in the 1031 exchange. 

The ones that are buying at 80-90% of ARV from wholesalers and hoping the market rises indefinitely are going to be in trouble. 

If you do a 1031 both the capital gains and depreciation recapture can be deferred indefinitely.  

I’m sure no financial investor would be willing to tie his asset to a non-owner indefinitely.  

This is purely anecdotal, but I personally have had multiple investor clients in recent months put their searches on hold--perhaps indefinitely--due to interest rates, economic uncertainty, and the losses they've taken in their broader portfolios.

National Home Price Index , I highly doubt prices will continue growing indefinitely. 

As @Paul De Luca mentioned, 1031's are a great way to maximize your investment power by indefinitely deferring all tax and depreciation recapture.

A co-worker of my realtor seems to think it renews indefinitely.

I plan to stay in NYC indefinitely but it's hard to predict when or if I'll want to move out of the NY area.

All of your options, if there are any, will be outlined in or determined the actual language in your contract.As for the financing contingency itself, the language is very important…-some finance contingencies automatically expire on a certain date, some simply give the seller the right to declare the contract void once the date passes and can go indefinitely if the seller does nothing, etc.Remedies for default will also be detailed in the contract.