Once you’ve established a Trademark - an exclusive right to use a name or symbol in connection with a business or band - how long does it last? Simple - It last as long as you continue to use it (in commerce).

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This is potentially indefinite - the Bass Ale trademark logo is the oldest registered Trademark in UK - 1876. The oldest in the US is Underwood Deviled Ham - 1870. That’s just the date of registration - the oldest known Trademark is Stella Artois, dating to 1366!

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Beer and ham. What’s up with that?

As a general rule (not a hard and fast law) - if you’ve stopped using a mark for 3 years with no indication that you intend to resume use, you are considered to have abandoned it. If you make it clear you are not going to use a mark again, it may be abandoned sooner. (CEOs - don’t tweet that you hate your brand name) 

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If you have registered a trademark you need to show the USPTO periodically that you are still using it in business - but technically don’t need to renew the trademark itself - just the registration.