The issue I believe is almost similar to Health Boost resetting player health instead of "maintaining existing", in other words the regen counter resets to 0 so no healing can take place. Since it is applied each tick, the code resets unless it is fast enough (Regen 5).

How to reproduce:

1. Make a gamerule loop point to a looping function, like loop:loop. (/loop/loop.mcfunction)
2. Create a secondary looping function and point to this function from loop:loop to contain all effect "cheats" like loop:cheat_loop. (optional, you could do this from main loop:loop)
3. Add the line (could target anyone, even the player): effect @e[type=wolf] minecraft:regeneration 1 1 true

Regeneration 0-4 (1-5) does not work for above. However, 5 does (6).
When applied normally through a non-per-tick method, it works as expected.