Question: Guitar tuning going down on stage… why?

I play in a rock band in small pubs. I’ve played the two last gigs with my Majesty, but it’s a pattern I’ve noticed with all my guitars, of many different brands and models. It always happens.

When I setup the guitar at home, it’s perfectly in tune. Fine.

As I go up in the stage, I check the tuning before the gig starts… all 6 strings are slightly lower in tune. I have to tune the guitar up.

Then I come back home. When I plug the guitar, all 6 strings are higher… and I have to tune them down again. It’s very annoying.

What could possibly cause this? Anyone with enough stage experience could clarify the phenomenon?