I've incubated cells from mice lymph nodes for 2 hours at 37 C for MHC II tetramer staining, in my samples I could not detect CD62L positive cells also in naive mice.
Yes, it is possible. Did you stain them prior to the incubation?
Perhaps you want to do a time vs. CD62L expression curve, taking aliquotes every 15 min, staining and fixing them to find the optimum incubation time for your experiment.
CD62L is a marker which is temperature sensitive also, with my experience I can say if you want to stain for CD62L, keep everything as cool as possible. Also any activation (generally at 37 deg C) will downregulate CD62L activation (or Shedding).