DIAGNOSIS The internal diverter valve seals are failing. This is a wear-and-tear part that directs water either through the filter or around it (for unfiltered). When the seals go, water leaks out the side.
FIX For the PFM400H, the fix is usually replacing the entire filter head unit. The internal valve isn't designed to be user-serviceable. Contact PUR customer support. They often send a replacement head under warranty if it's within 1-2 years of purchase.
IF THAT DIDN'T WORK Before you conclude it's the valve, make sure the leak isn't actually coming from a higher point and just running down. Dry everything thoroughly, then run water while watching closely. If it's truly seeping from the seam around the plastic switch lever, it's the diverter.
HEADS UP Using hot water with this filter can accelerate the wear on these plastic internal parts. The PUR faucet filter is only rated for cold water use. Running hot water through it can warp seals and cause this exact leak.