Assembly unable to locate file even after manually browsing for file

Is the path.sldprt file a component in the assembly, or is it an external reference to one of the parts or assemblies?

Reason why I ask, is that, if it is the 2nd one, then you need to make sure that your references aren't locked for that part that is linked to it and then make sure that you save that particular part as well.

John,

I take it you're saving the assembly after you have manually located the missing part?

John,

Have the part you want to use open first.  Then open the assembly.  Make sure you save the assembly to update the references.  Also, make sure that under tools, options that you don't have a references document location that pulls the part you don't want.  

Sounds sort of like what I posted here Locate/open replace file  and still unsolved.

you can save a copy of the Part file (different Name), in the Assembly replace the current Part with the Copy. this is not the elegant Solution, just a work around.

After clicking "Browse for file", then locating the part, the next time I open the assembly solidworks asks me to locate the part again

the part you mentioned here is in the main or sub assembly

if it's in the sub-assembly, you need to open and save the sub-assembly otherwise, it'll ask you again next time you open the main assembly