How Can I Do This

Have a command block system check when someone dies. For more info check this answer. (It’s for the bedrock edition but should still work, instead of testfor use /execute if). Obviously change the selector form an @e zombie one to an @a. When someone dies you can then run a command that is to take away the strength. You can then use a comparator and repeaters to make a delay and then give the selected player strength again. A repeater set to 4 ticks gives a 0.4 delay, so use 62 4-tick repeaters and 1 2-tick repeater for 25 seconds.

Limitations

If someone leaves the kill cooldown will reset.