After setting player regeneration effect in a newly created world like so:
/effect give @p regeneration 1000000 255 true
regeneration works fine. You can see the jumping health heart animation and player damage is limited / not severe. I then save the game and exit.
Later, I will reopen the launcher, and choose the game I previously saved. The jumping heart animation is shown and the effect is listed when viewing the inventory (without the recipe book open) but the regeneration effect itself is not enabled and player receives damage as if no regeneration is enabled at all.
Regeneration settings elsewhere were not adjusted.
Difficulty mode is Normal
No resource packs or mods (vanilla install).
The only other cheat I entered along with regeneration is:
/effect give @p night_vision 1000000 255 true
Related issues
Comments

@tryashtar, the link to 'Potion effects' wiki in the issue you linked to has no content. How would I know about this? The game should present a warning if you use a multiplier over 127. I agree with some of the posters in that thread: the game should warn that any multiplier over 127 is wrong. Smells like a bug to me.
See MC-10755. Do not use effects greater than level 127