We recently moved into a new home and when we installed our outdoor lights, we noticed that the outlet wasn't receiving any power. We checked the other exterior outlets, and those too were dead. We reset all of the GFCI's that could be affecting it, and that didn't help. Next we replaced the GFCI and that didn't help either. Lastly, we replaced the breaker switch and that didn't work either. Do you have any other suggestions for what we can do to fix this?

Sounds like you checked all the typical reasons, so there must be a loose splice or connection is the circuit somewhere between the panel and this outlet. Each outlet and junction box will need to be opened to check for a defective connection on one or both of the hot and neutral wires.

Could be fed from a switch. Identify all switches. Most will be easy.
Plug in an extension cord into a known working outlet. Bring meter and other end of cord to bad outlet, verify at end of cord, 120 between hot and neutral(Hot is small opening), now place meter in known good hot, at end of cord, now plug meter in bad outlet Neutral, if you now have power, Your neutral is good, also do second test to see if hot is good.)Maybe neutral opened)
If you lost hot and neutral, and ground still intact, Most likely load side of a gfi, Maybe in a bathroom, or an odd looking one in the Panel.

If you lost all 3(Hot, neutral and ground)Roofer cut through with saw, Don't Ask