Most people with Bell's palsy will eventually recover fully. About 80% of people with Bell's palsy will recover fully by 6 months (most in the first 8 weeks) after onset of symptoms. Others may recover more slowly. Steroid therapy is proven to speed the rate of recovery (all-comers, not necessarily in any single patient); but that recovery does not necessarily have to begin while on steroid therapy. (It can be after steroid therapy is completed before one may notice improvement.) Furthermore, even without steroid therapy, most patients will recover fully. There is no evidence that treating with a second course of steroids is more beneficial than the first course.
If his Bell's palsy does not seem to start recovering, consideration should be given to whether his Bell's palsy might be due to some specific condition such as "sarcoidosis" (a chronic inflammatory condition that requires long-term therapy and can involve multiple organ systems), Lyme disease, some form of malignancy (i.e. cancer), etc. Although the latter sounds bad, the vast majority of Bell's palsy is "idiopathic" (though thought to be due to a viral infection of the facial nerve). If the Bell's palsy was due to sarcoidosis, more steroids may help (by stopping the "attack"); but if due to a viral infection, the virus has already run its course, and the facial nerve has already been damaged and will have to "regrow," so more steroids won't help.