Does DeskOps follow up on a quote nobody answered?

Yes, twice: a follow-up three days after the quote went out, and another at seven days, each with the link to accept. They stop the moment the quote is accepted, declined or expired. Quotes carry an expiry date so an old price does not stay open forever; the default expiry is set in the quote template and can be changed on each quote. Sending the same quote again does not change its price, its expiry or its number.