I’ve been noticing the same telemarketing numbers over and over on our caller ID. We don’t answer the phone when they call. How long does it take for a telemarketer to give up on a particular phone number?
Never, if you don’t answer they’ll just shuffle your number into the next rotation until they get something, negative or positive.
Best bet is to pick up the phone and tell them to put you on their do not call list.
Tell them to put you on their do-not-call list. They pay hefty fines if they call you after that.
Though some people have had success with those devices that mimic the tones that the phone company plays before the message that a line has been disconnected.
If enough people start using them though, the telemarketers will reprogram the tone-recognition on their auto-dialers and we’ll be back to square one.
There’s no federal rule about how many times a telemarketer can try a number before giving up. It’s up to the individual company to decide how many tries is cost-effective.
If you’re feeling really evil, and have some free time and any amount of willpower, answer, and see how long you can keep them on the line without buying anything. The way they make their profit is based on the assumption that calls that don’t result in sales will end in the first 2 minutes or so. Keeping them on the phone for inordinately long ammounts of time and still not giving them a sale cuts into their bottom line.
How do you know its a telemarketer? WHen they call me 80% of the time their number shows as ‘unavailable’ on my caller ID (which is a real clue it’s them).
Maybe it’s someone from the lottery saying you won? 
I’ve been experimenting with the question posed in the OP, and can say with some confidence that “six months” is about how long it takes.