Strikes me the finger of suspicion is pointing at:
The second unit:-
Input: 230V
Output: AC 110V 45VA
The table, motor and keypad controller are OK because they started working again after replacement power supplies were received.
Steve: to eliminate any doubt did you replace both power units or just the 230 to 110V converter? (Ideally just the 230 to 110v unit!)
That the unit ran for up to 1½ hours suggests something is overheating. As Michael remarked, it's feels odd that Sherline are running a 2A stepper and controller from a 24W DC supply, but they probably know what they're doing! Anyway the web isn't full of complaints that the unit is unreliable, and there's no mention in Michael's pdf instructions about allowing cooling-off time.
I'm suspicious of the 45VA unit, which is also on the weedy side. It probably contains a small transformer protected by a thermal fuse. If the transformer gets too hot, or the fuse is oversensitive, it will cut out. These things are usually sold as travel accessories, for example so a 240V UK electric shaver can be used in a 110V US Hotel Room. Maybe you've been given a unit designed for 10 or 15 minutes shaving, and it can't cope with an hour's solid work? (How hard are you working the table – roughing out spokes on a big steel flywheel or delicately putting teeth on a thin brass gear? If the former, don't forget the Sherline is a dinky little machine, not a chop saw!)
If the item is under warranty, speak to the supplier. Otherwise, 240 to 110V converters are inexpensive. You could try one rated for 100W, or even 200W like this example.
Dave