Bankroll management is a way of keeping you from losing all the money you are willing to put towards a poker in a certain period. If you are not willing to make a redeposit at a certain site, then you should follow the regular bankroll rules with whatever finds you deposit to that site.
If you're willing to move funds around, then it doesn't matter unless it will effect your play.
That is, if you get low on one site due a cooler and you start playing worse poker (maybe tightening up too much) simply because you fear losing your last few buy-ins, that's bad.
But if you're capable of playing your best game, and shifting winnings from other sites to the site you were unlucky on (or completely abandoning that site) then it's not so bad.
But look... it all comes down to it being your money. Do what you want with it. I have a friend (he moved away recently) who was a consistent loser online, yet he kept sinking hundreds of dollars into it because he had a good time. People pay to play golf, he paid to play poker. The enjoyment he got out of playing was worth the money.
So do what you want. But if you want to avoid going broke (without redepositing) on a particular site, make sure you have the proper bankroll for your level of poker deposited on that particular site.