From what I remember is they don't delete, you just click on your user profile and click on the tabs for either Mentions or Quotes and you will see the very newest quotes or mentions up top with date and time everyday.
As more quotes and mentions happen the older ones lower on the page and will separate by the next days date.
If you see my pic of quotes and mentions below, you will see Tony mentioned me yesterday and the time and date separates the last 24 hours of mentions and quotes.
I like that they are always there day after day if I should need to look up anything.