C. elegans is nice for this since you can freeze stocks in glycerol. Labs routinely go and thaw out the main wild-type reference stock if the lab stock has been around for too long.

Now I'm in a fly lab and no one's really figured a good way to freeze a fly stock down for long-term storage. So we're left to just accept some degree of background mutation and generally assume that it's not impacting our experiments too much...