I have a bike with back-pedal brakes and recently the chain keeps slipping. I've tried just putting the chain back on but about two or three weeks after it will happen again. I've tried moving the back wheel further back but this is only a temporary fix as well. The chain is dirty but well oiled. The back wheel has just been replaced and the teeth on its cog are new. I've been told that the front cog's teeth could be too worn (although not whilst talking about this particular issue) but they are probably about 7mm high and don't look that different to the teeth at the back.

Does anyone have any suggestions?

When have you last changed the chain? Measure the length for 12" down to the nearest 32nd of an inch.

Do the front and rear sprockets line up as best you can tell, or is one offset from the other a bit?

How tight is the chain? I tend to like a fair amount of tension. It probably doesn't need to be tight, but certainly shouldn't be sloppy loose.

Thanks for your response. The chain is tight but hasn't been changed in at least 18 months (which was when I bought it second-hand). I think it all looks aligned.

Is the chain coming off from the front ring(chainring/wheel), or rear sprocket?

New cog with worn chain will skip. Measure the chain for wear ("stretch"):

Nice video. It may be a little easier to use the edge of the pin as the reference point (same edge, R or L, at both measurement points, obviously) instead of eyeballing the center. Six of one...
Steve