Nope that's incorrect the max limit for CAT5e is 100 meters not 125 feet that's 38.1 meters which is well within spec
as for the disconnects that sounds like an overheating router make sure it's in a well ventilated area you could also sit a box/floor fan next to it so there's good air movement past the router if it stops disconnecting you know it's overheating
I've had routers that have small heatsinks on the chip be knocked of through rough courier handlin and continuosly over heat until it was put back on properly