It depends. A lot of the grounds don't have a time component, but if you've voluntarily lived with the person after the ground ended (being released from effects of it or learning of it), then you probably wouldn't qualify for the annulment.
Grounds for annulment include
• influence of alcohol or narcotics
• fraud, duress, or force
• mental incapacity
• concealed divorce (only usable until one year anniversary)
There are also a few other REALLY obscure ones. So it would be hard but not impossible and all very fact-specific. I'd strongly suggest you hire a family lawyer to help with this if an annulment, rather than divorce, is important to you. It will be tricky.