I notice in the console log that it's spitting out multiple reload messages at once.  I made a brand new project with literally just GMLive imported into it (so the only object is one instance of obj_gmlive placed inside Room1) and when you run it the console Output says:

**********************************.
Entering main loop.
**********************************.
[live][7/28/2020 10:09:06 AM] Ready!
[live][7/28/2020 10:09:07 AM] Reloaded obj_gmlive:Draw_0.
[live][7/28/2020 10:09:07 AM] Reloaded obj_gmlive:Draw_0.
[live][7/28/2020 10:09:07 AM] Reloaded obj_gmlive:Draw_0.
[live][7/28/2020 10:09:07 AM] Reloaded obj_gmlive:Draw_0.

It prints that message from 2-4 times generally.  Interestingly the gmlive-server.exe shows:

ready! 4 live files, 0 globalvars, 1 macro, 0 scripts, 0 enums. Took 76ms (and says 1 client)

And if I just end the program and literally re-run it without changing or doing anything, it goes:

**********************************.
Entering main loop.
**********************************.
[live][7/28/2020 10:09:06 AM] Ready!
[live][7/28/2020 10:09:07 AM] Reloaded obj_gmlive:Draw_0.
[live][7/28/2020 10:09:07 AM] Reloaded obj_gmlive:Draw_0.

ready! *2* live files, 0 globalvars, 1 macro, 0 scripts, 0 enums. Took 56ms (and says 1 client)

So the number of "live files" seems to be random each time it's run. This is a completely empty project so it should be easy to reproduce!

I'm having the exact same issue since upgrading to 1.0.26. It seems the longer I leave the GMLive server running, the more times it reloads all my files when I start the game, sometimes it even times out entirely.

[47fe74c6|127.0.0.1:52198] ready! 16 live files, 0 globalvars, 55 macros, 228 scripts, 20 enums. Took 1361ms.
[0c72fd6a|127.0.0.1:52622] ready! 24 live files, 0 globalvars, 55 macros, 342 scripts, 20 enums. Took 1815ms.           
[47fe74c6|127.0.0.1:52393] timed out.                                                                                   
[0c72fd6a|127.0.0.1:52633] timed out.                                                                                   
[054bf51f|127.0.0.1:52792] ready! 32 live files, 0 globalvars, 55 macros, 456 scripts, 20 enums. Took 5043ms.

This is fixed in 1.0.27+