It can be used whenever you like. You can use it immediately, or you can hold on to it for months. Yes, vouchers can be used in other sessions, even after the initial session expires.

Let's say I deposited 0.1 BTC a month ago, and then immediately withdrew a 0.064 chip and kept the other 0.036 as a voucher. Now, a month later, I open a new session. In that new session, I can make a new deposit (let's say I deposit 0.04 BTC) and I can also redeem my old voucher, meaning my new session will have a total balance of 0.076 BTC. I can redeem multiple vouchers and combine their values, and I can leave behind what I don't withdraw in a new voucher to be redeemed in another few weeks or months.