I have outdoor lighting plugged into 2 outlets in the front of my house. On several occasions the lights did not come on and I found an outlet in the back of my house that needed to be "reset". The lights would then work for several weeks and then it would happen again. Now the lights will not come on at all. I replaced the plug in the back with the "reset" but it still does not work (the outlet in back still works but the front ones with the outdoorlighting do not... ). I have checked my breaker box and found no problems. I plugged a small radio into the outlets in front and it did not work so I know it not the lights.

Any advice would be appreciated!

It's the wiring that has a short in it. You need to take a multitester to see if you are getting the proper voltage through the wiring into the outlets. If you are not getting the proper voltage your wiring is done for and needs to be replaced.

If all of these outlets are on the same circuit and apparently they are, and if the GFI works but the other outlets do not, I would say that you errored in replacing the outlet.
If you press the test does the GFI trip off. If you manually trip does the outlet still have power.
Check your work. Ensure that you have the hot side connected to the line side terminals and the wires to the front outlets connected to the load side, GFI protected, terminals.

I am confused by this sentence "I replaced the plug in the back with the "reset" What plug did you replace? Can you explain further? You obviously have a GFCI outlet in back and the fronts are likely tapped into it. If done properly this will give GFCI protection to all of the outlets as Harold has explained. If that pluged you replaced was actually something like an extension cord to the fron I'd say you messed up with the installation of the plug. Back to you for further details.

I hope you are unpluggin all cords during test, they may be the fault, like above, be sure of line and load and correct polarity(hot to hot and neutral to neutral).
Your wiring is likely not "done for", usually connections.