outside outlets stopped working.?

Does your outside circuits have a ground fault plug in the line someplace? If so it may be tripped or needs replaced. 

I have two outside outlets that are on the same line which are not working. The breaker in the panel is not tripped, resets fine. ... Typically, only one GFCI outlet is needed *IF* the outlets are chained together on the same circuit breaker (but it is OK for each to be GFCI).

Check to see if any of them are GFI outlets. If one is popped it will turn them all off.

Have you checked to see if one of the outside outlets is a GFCI outlet itself?

Also check outlets in the kitchen, or anywhere else with plumbing. The outlets could be protected by a GFCI outlet you don't use enough to remember.

This situation is serious enough to call in a licensed electrician.