The good news is that nowadays you can see when your miles expire in your Aeroplan online account. It clearly tells you this under Personal Information and even in the overview.
What you might not know is that you can reinstate miles when the expiry date lapses. According to the Aeroplan help page:
"Expired miles are eligible for reinstatement up to 7 years following the last accumulation or redemption transaction in the account, whichever is later. You may reinstate a portion or all of your expired miles for an administrative fee of C$30 plus C$0.01 per mile reinstated (plus any applicable taxes). Reinstated miles will be available for redemption for 7 years from the date of reinstatement as long as you remain active in the program."
Seeing that it adds up to $100 per 10,000 miles, it's probably a good idea to use up your Aeroplan points prior to the expiry date.