Notice that you have a tire with a slow leak? One easy thing to check first is the valve stem, the core may just be a little loose.
There are a bunch of tools for tightening valve cores, some valve stem caps even have little teeth on the back side to remove or tighten cores. I have the Valvecapper, core tool on one end and grippy end for removing valve caps on inner duals.

There are a bunch of tools for tightening valve cores, some valve stem caps even have little teeth on the back side to remove or tighten cores. I have the Valvecapper, core tool on one end and grippy end for removing valve caps on inner duals.