Does focal radiation for prostate cancer weaken the immune system?

Not really: I'm not sure what you mean by focal (brachytherapy?) but with either external beam radiation or brachytherapy men do not routinely have their blood checked to follow their blood counts during treatment because the risk of having them decreased during radiation treatment is so low.

Possibly: External beam radiation is given to the prostate only. With modern techniques of imrt and igrt the radiation is spread out significantly over the pelvis which houses 40 percent of the bone marrow. The bone marrow is sensitive enough that in some patients we see a lowering of the white count and thus weaker immune system. This usually is very minimal and easily recovers on its own.

Immunity and XRT: Twenty five years ago we checked white counts(immune system) on every patient receiving radiation every week. We found very few of the patients had a decrease in the wbc. The patients that did had large volumes of bone marrow in the radiation fields. Patients getting chemo of course did too. Treating the prostate only will not result in a decrease in wbc.