My MacBook Pro 13'' works only with 85w charger
Either:


The two Macbook 13 draw different power due to normal conditions and your adapter won't work at all when a normal but high draw is needed. (i.e. replace your adapter)
The 60 W adapter is failing and it' bad luck that you got a few heads in a row and a few tails in a row - if you do enough tests 50% failure rate will happen with any MacBook. (i.e. replace your adapter)
Your MacBook is drawing / requesting more power than it should and needs a soft reset / SMC reset or repair. (i.e. service your Mac)