Loose toilet handle question

Some months ago, I noticed our toilet handle on our 30 year old bathroom toilet was loose. It could have been the original handle on this toilet, I don't know, but upon opening the top tank lid, I saw the handle nut had become loose. I tightened it and within a week upon inspecting, I saw it had become loose again. So, I just took the handle, chain, etc. out and replaced with a new one. It seemed to be working fine, but this morning, upon inspecting it, I saw this handle's nut loose again. Now, I should mention that I hand tightened the nut upon installation and gave it an extra little bit of 'force" if you will with my hand, nothing major but I didn't use a wrench with the nut for fear I might damage the porcelain by tightening too much. My question is, since it's worked itself loose again after a few months, is it recommended that I tighten it with a wrench this time (and if so, how much?), or has the porcelain behind the nut worn away to where it's not making a good tight hold? Thanks in advance for any assistance.
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replacement may have a bit too much slop where the stem doesn't fill the handle hole, allowing nut to more easily wiggle its way loose. there are a variety of handle sizes, shapes, and arm lengths. perhaps just add a dab of silicone seal to the dry threads and screw the nut back on.
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Just give the threads that show beyond the nut a good aqueeze with a pair of pliers to deform them and the nut will no longer back off easily.
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