Try Consumer Cellular through AARP. tHEY SAY THEY HAVE PLANS STARTING AT $10 PER MONTH.
Hard to find plans with minutes that do not expire, IMO.
1-800-283-3118
AARP Cell Phone Plans from Consumer Cellular
Not a subscriber, since I'm contracted to Verizon, just reading from an ad that I received in the mail.
Looks like you can have a 45-day free trial. In reading somewhere else, I believe that the serice is provided through AT&T.