Here's an example to demonstrate your dilemma. IBM closed at $152.50 today. Assume that the closing quotes are accurate and that you trade at the market (though a roll spread order should do a bit better).
Suppose you are short the 3/29 $152.50 put which closed at 94 cents (ask price for BTC). It's ATM and will expire tomorrow. Perhaps IBM stays above $152.50 and you'll get to keep it. Perhaps not.
Let's pretend you could transact right before the close at these quotes. You could roll your short put out a week now in which case you'd get a credit of $1.16
Now suppose 1 minute later IBM dropped $2.50 and your put is now $2.50 ITM (with no change in IV). The $155 put would simulate this. Now, the roll is on worth a credit of 76 cents ($3.45 - $.94).
As you can see, the further your put gets ITM, the less the credit will be, hence the reason for rolling before that happens. And FWIW, if your put got $5 ITM, the credit would be only 20 cents, hardly worth the effort.
So if you have em, roll em... or if you prefer, close em. But don't let them get well into the money.
3/29
152.50p 0.87 x 0.94
155.00p 2.46 x 2.69
4/06
152.50p 2.10 x 2.19
155.00p 3.45 x 3.65