I still use points on my MGB - and I have never really had a lot of trouble with them if they're replaced and gapped correctly.
*However* I have had a lot of grief recently with what turned out to be a duff rotor arm - there's a lot of this about at the moment it seems - car runs for 20 minutes or so then packs up and won't restart until it cools down.
Turns out that the worst offenders have a rivit holding the copper blade in place and are black (too much carbon in the plastic) and when they get a bit old and/or hot they break down.
Look absolutely perfect to the naked eye but they short out when hot.
Made worse when people upgrade to electronic ignition and powerful coils because the voltage goes up and they brake down more easilly.
I'd deffinately recommend having a spare rotor arm in the glove compartment and check to make sure there's no rivit in it and that it's red rather than black.
After the fact I found out about it here:
http://www.distributordoctor.com/rotor_arms.html
available here too
http://www.simonbbc.com/rotor-arms
actually there are black ones on that page too with a screw or rivit they look like the type to avoid!