Chain keeps slipping on in-hub geared bike. Stretched chain?
Chains do not literally stretch, i.e., the metal links do not actually elongate due to  the force placed on them. A chain will get slightly longer as it wears though, caused by the holes in the links the pins go through getting slightly bigger, allowing the individual links to move slightly further apart. 

Here's a good article on chain wear: http://www.bikeradar.com/us/road/gear/article/bicycle-chain-wear-explained-46015/

If you ride a lot, your chain might be worn out and this has worn the rear sprocket as well, causing the chain to slip over the teeth.

See this question for diagnosing if you rear sprocket is worn out: How to tell when to replace cassette?

However, in your question you say that the problem went away when you adjusted the chain tension, then came back when you rode the bike. It may be that the wheel had slowly moved in the frame over a period of time until the chain started slipping, then you moved it back but did not tighten the wheel sufficiently allowing it to move again (and more than before) when you rode the bike once more.

If the wheel moved you will see that the chain tension is now too low again. If you do not feel happy tightening the wheel in the frame more, or don't want to risk stripping threads on the axle or nut, have a bike repair shop adjust the chain tension and tighten the nuts to the proper torque setting with a torque wrench, and check the chain and sprocket for wear at the same time.