Cold start solinoid (sp), perhaps, is shot... It provides extra gas to the engine when the engine is stone cold... I think that the little driving you do at 20 mph is enough to warm the engine just enough for it to not kick in with the extra fuel on the restart... If the engine is sufficiently warm then it isn't needed but until that temp is up to the middle of the guage, which with the little driving you are doing, iy prolly isn't, I think that is it...

B~ (Motorhead)