Roger (not David, AFAIK) and P.H. along with former Gin Blossoms lead guitarist Scotty Johnson have gone on to form another band, Roger Clyne and the Peacemakers.
The Peacemakers have a decidedly more country flavor than the Refreshments did, but the style is pretty similar.
They have a website at

Ed. Note: IMO, the Refreshments wrote some of the best driving songs ever. Great stuff.