Does Roland Banks' weakness Cover Up get discarded when I've removed all 3 clue tokens from it, or do other weaknesses get discarded when they are done with the instructions on the card? There is no mention of it so my thinking is that I do not have to discard it and potentially end up drawing it again once I've resolved a card such as Cover Up.
Weakness (or treachery) cards go to your discard after being completed. Page 20 of the RRG:
When a treachery card is drawn by an investigator, that investigator must resolve its effects. Then, place the card in its discard pile unless otherwise instructed by the ability.
Further, on page 7 of the RRG (emphasis mine), pertaining to weaknesses that are enemies and can be defeated:
if an enemy has damage equal to or higher than its health, it is defeated and placed in the encounter discard pile (or in its owner’s discard pile if it is a weakness).
Non-enemy weaknesses specifically say on the card what to do with them. For example, Cover Up says:
When you would discover 1 or more clues at your location: Discard that many clues from Cover Up instead. Forced - When the game ends, if there are any clues on Cover Up: You suffer 1 mental trauma.
This means that Cover Up stays on the table (with no clues on it) until the end of the scenario.
In contrast, Daisy's weakness (the Necromonicon), says:
...if The Necronomicon has no horror on it, discard it.