Sounds like a flat head cap screw. Make sure you are using a quality allen wrench that is the correct size. Some cheaper made tools might not fit as well in the hex socket of the screw. Also, use a wrench with the shortest possible length—the farther the wrench sticks out of the socket, the greater the chance it will twist and break. When trying to turn the screw—push the wrench completely into the socket, and hold it there while applying torque—any misalignment can result in the wrench stripping out the screw.
If all else fails...get a left hand drill and drill out the screw. 23 years in a machine shop...pulled out a few stuck bolts and screws...
Thanks for the excellent advise. I wouldn’t call myself a “wrench”, but I’ve turned a bolt or two in this life and know you speak sooth.
I’m going to first try some of the penetrating oils folks have suggested, then take it up a notch up if needed. Thanks.