Can battery testing damage the battery???

[blau]

I have an old battery show 2v and I charged it up with a 1.5amp trickle charger took about 2days. I then use a old fashion battery tester on it it was marginal. So I cycle the battery discharge it to about 11-10.5 v with a headlight and charge it back up again. for about five times. It tested still marginal. Voltage stabilized at 12.4ish volts.

So I decided it to cycle it a few more times. But this time I test it this way using the battery tester I tested it 1st time for 7 sec and wait a few sec test it a 2nd time and wait a few minutes and test it 2 more times a few minutes later then discharge.

But the battery is worst then before. It is testing lower on the battery tester no longer marginal (it is testing bad) and voltage stabilized at 12.1ish volts. I cycled it a few time since not better.

So can you damage a battery by repeating testing with a battery tester???

Does anyone have an idea what is going on here???

Any ideas on how to repair the battery at this point???

thanks