Six months is common and it's negotiable. Nothing in the settlement rules sets a term length. What the rules require is that a written agreement exists before your agent tours a home with you, and that it states the compensation clearly, in a specific amount or a specific formula, rather than "whatever the seller offers." Length, geography, and exclusivity are all just terms in a contract that two parties agreed to.
So you can ask for 30 days. You can ask for one property. Some brokerages have a house policy on minimum terms and some agents will decline shorter, which tells you something useful about how they work.
On being stuck: read the termination language, because that's the section that decides it, and it varies by brokerage form and by state. Some forms let either party cancel with written notice. Some let you cancel but keep the agent's claim alive on any property she showed you, for a stated number of days after the agreement ends. That last one is what @harrow is describing, and it's the clause most people don't notice until it matters.
The piece worth raising while you're still negotiating is what she does if the seller offers less than her stated fee, since that offer no longer appears on the MLS and gets found out property by property. Get that in the same document. If you want a legal opinion on whether a specific clause binds you, that's a question for a real estate attorney in your state, and it's cheap compared to a commission dispute.