The use of a cell booster may help your service at home but not between your home an where you loose service.
Because the phone is not finding available service once in the area is should work I would think the phone may be having some issues. The OS controls the operation and doing a reload may help. You will need to do a backup of your contacts and other apps first.
You will need to download the available OS to reload unless you have a copy. This site has a forum section where 4.50.313 is shown. Also the section offers information on doing updates or replacements. Latest OS: 8300 220.127.116.113/18.104.22.168 (Multilanguage)
Because you reloading the radio and it does not help, I think it is pointing to the basic OS..