I had been running a Raspi B happily using a generic 5v power supply until I recently added a USB 3G modem. I then started to get a series of problems (modem would stop working, Raspi would freeze or crash) until I replaced the power supply with one that came with a Raspi 3. It’s been running for 3 days constantly with no problems. Just thought this may help others thinking “it can’t be the power supply”!
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Many thanks for sharing. One interesting point would be if you ever saw the lightning symbol (top right corner) when any of the issues happen?
I was actually running the raspi headless for a non-OSMC project but I thought it was so relevant to many of the problems reported on the OSMC forums I would share it here. 
No worries, and yes this is good information for everyone