Yes definitely. I usually attempt to wash the yeast by letting it settle, then pouring off the discoloured fluid left, & then topping up with filtered water. Usually I do this 3, maybe 4 times, before the fluid remains clear after the yeast re-seetles. Obviously I shake the storage jar after adding water & the whole process is kept at refrigerated temperatures. My storage jar is lidded, but not a pressure resistant seal.
I cannot reliably advise you on the life of the yeast culture in these circumstances, but would expect several weeks as a minimum. I also do not know if what I term washing (as above) is necessary or not. Finally most home-brewers I talk to, about keeping a yeast culture like this, limit the number of "uses" to 3 or 4. My best judgement is that so long as you keep producing a sound brew, free from "off", or other unusual flavours, keep going.
Pete