I will describe my bike 'problem' so you can see whether it fits with your problem. I know what the reasons are and how to solve them, so it is not an 'I also have this problem' answer.
I have the problem of a slipping chain and on my bike it is clearly a tension wheel that moves out of its place, so in fact the chain is not tensioned enough.
The slippage starts when there is stress on the chain, like when riding away from the traffic lights and on the steep parts of hills.
When the wheel moves a bit more/the chain becomes a bit longer compared to what is should be, the slipping becomes more general, if still worse when trying to increase speed.
In the last stage, the chain jumps in every stroke of the pedals and cycling becomes impossible. (Then I take out the tools and fight the system so the tension wheel will be in the proper position for a while.)
Unless your bike is in the 'last stage' you will not be able to copy it on the stand as you do not put the same amount of power on the chain, so do not get the same stresses on it.
This is on my recumbent bike, which has a long chain and is designed for lots of adjustments for different riders.