I took a look at the "Terms of Service" and the "Acceptable Use Policy" posted on the namecheap website, and I don't see anything that would prohibit faucets or bitcoin mining.

Did they provide you with an attachment in the email with evidence that the activity is prohibited?

Perhaps, take the word "faucet" off your website and let them know that you've changed the site.  Tell them it is no longer a "faucet", and that now it is just a simple "pay-per-click" advertising site?

EDIT:  Thanks to Nixtren for linking to the AUP (Acceptable Use Policy) that specifically bans bitcoin mining.