All that aside, one common thing you will read from many of us here is that VFDs are really good at finding problems that less sophisticated devices, like basic overload relays, will let slip by. So it's entirely possible that the VFD was seeing something that it knows will result in motor (or VFD) damage and it tripped off line to prevent it, but the OL relay in your bypass setup is nowhere near as accurate, so it will wait until the failure is more "complete", kind of like an idiot light. And of course, this ASSUMES that your bypass system even INCLUDES an overload relay. I see a LOT of people who don't catch that detail and just use a manual bypass switch to jump around the drive. That's not going to meet Code, and the MFR (assuming it was Sq. D) would not have done that for sure. But when people "roll their own", they do all kinds of goofy things.
Also, in the VFD world, "Overload" can mean MOTOR overload, or DRIVE overload. In the Altivars, if they just have the cheap little 7 segment LED display and not the nice LCD full text display, you have to read the "code" on the display. For example, "OHF" means DRIVE over heat, "OLC" means PROCESS overload, "OLF" means MOTOR over load, and "OCF" means over CURRENT, which is different than over LOAD. Of all of those, the "OCF" fault is the only one that looks like an "Overload" and cannot be reset automatically, meaning someone must actually find the problem and fix it. OCF can be triggered for example by someone trying to over aggressively accelerate, which means the motor tries to draw more current than the drive can deliver safely.