"Some period of time" is using "some" to make reference to one period of time that is unspecified. "Some periods of time" is plural. The use here is akin to "Some dog just bit me." It's an unidentified single dog.

I will be going in and out of cell coverage so I will be unreachable for some periods of time. (I expect there to be several different periods.) We're passing through a region where there is no cell coverage. I will be unreachable for a period of time. (There will be one period. This would be my slight preference.) We're passing through a region where there is no cell coverage. I will be unreachable for some period of time. (There will be one unspecified period. Natural. Pretty much the same as "a")