[Jeffhs]

If this radio plays well only on strong local stations and doesn't pull in distant ones, even after sundown local time, I'd say it probably has a bare-bones chassis with no more than four transistors; that or else, if it has six transistors or more, it may be far out of alignment. Another possibility is the battery is weak or nearly dead. I'd try the radio with a new battery before doing anything drastic. I have several battery-powered transistor radios here that won't work worth a darn if the batteries are the least bit low; since I am 33 miles east of Cleveland and the radio and TV station towers are about 10 or 15 miles further to the southwest, I notice it when any of my sets' sensitivity drops. When the batteries are good, I can get every Cleveland station here as well as if I were still in the suburbs; however, let the batteries go down to, for example, three volts for a 6-volt set and I lose just about everything but a 1-kW local station five miles away.

OTOH, your little portable radio may have been designed purposely with low sensitivity, for use in near-suburban or urban strong-signal areas. It sounds to me like this radio may have been a promotional item given away by radio stations during live-remote broadcasts.