Is your house older? Older homes will often have this setup with multiple things on one GFCI. Some things will cause them to trip as a nuisance. Some times they wear out.
There is an easy way around the problem that still provides the protection (I do think GFCIs are a good protection device to have.) You can wire a GFCI outlet so that it protects either the whole circuit or so that it protects just the outlet it is installed at. When you look at the back of the GFCI you will see two sets of screws, one labeled Load and one labeled Line.
The hot wire coming in to the box always goes to the Line screws. If you attached the wire to the next outlet to the Load screws, the GFCI will protect outlets downstream (this is how yours sounds to be installed and the typical way.) If you attach the downstream wire to the Line terminal (there is a place to do this) then you will always have power downstream, but the GFCI outlet itself will be protected and trip off if required without interrupting power downstream. If you set it up this way you need to install a GFCI outlet (wired to the same way) at each of the outlets requiring the protection - bathrooms, garage, exterior, kitchen etc (anywhere around water sources) to maintain proper protection. Note: you have to wire it this way, if you install additional GFCI's but wire them the other way, the first one will still tend to trip and you end up with a confusing mess.
In older homes where the circuits were not specifically designed for GFCIs it is common for there to be things on the circuits that cause nuisance trips. This method solves the problem and is easy to do. Just costs a little more for materials.
Kevin Weiss
AbsoluteInspections.net