The best and surefire way to counteract this is to increase your income....

The old house ended up used for storage, campouts or whatever until it eventually decayed to the point where it had to be burnt or dozed.This is the real meaning of depreciation. 

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Bodies will explode if they are left to decay and fill up with all sorts of gases.

go to homepath.com and see if you can find the contracts and print them up. i have not worked with many of them ( i am a licensed agent so i have worked a few deals with them, none investors so i don't normally read to much into that clause ) but somewhere in the counteract/adendum it will say when you can and can't sell the house.

The best way to counteract this, is by knowing your market well enough to understand what's too much.

You can use losses from depreciation to counteract other other real estate gains across your portfolio.Would your house make 20%+ more money if you rented it room by room on 6-12 month leases?

I mean it would be nice to counter act the price and cost of the mail and time.

If necessary you can chisel out some decayed spots but it is something you can do yourself or hire an apprentice mason there. 

This is just an example, but in my opinion the aspect of holding onto a flip for a short time, counteracts the some of the risk in using your cash.