"You will have 10 BTC expire next month"

So you spend it.

Also, once the BTC expire, they don't disappear. They are made available for mining. This is possible because the block chain has full history.

In order to spend bitcoins, you need someone willing to exchange them for goods or services. Why would anyone do that if the bitcoins they received were going to expire?

For instance, let's say I wait until the literally last minute to spend my expiring bitcoins. I want to exchange my almost-expiring 10 BTC for $100. Would you accept this offer, knowing that those 10 BTC will vanish shortly after you accept them?

I was not clear. They only expire if YOU don't spend them.

Once you exchange your 10 BTC, the expiry date is reset.

So what's stopping me from creating multiple accounts and swapping bitcoins between them to prevent them from ever expiring?

Nothing. I didn't say I've thought it out completely :)