I mixed LPD for a printing session in October. I printed then, then again a month later in November. Then I didn't get to print until January - same one quart (quart, not a gallon) bottle of working solution, not even topped off, still working. Color is slightly darkened but not that much and activity seems unchanged. This coming weekend I'll probably either mix fresh out of an abundance of caution or at least top it off with fresh as it's down to maybe 3/4 the original amount just from what the prints have carried out into the stop.
LPD has been my favorite print developer for decades.