Hi
Great question, but it's really hard to answer without knowing what service you provide. Also, it really depends what percentage your talking about - if its low - I wouldn't waste time on it for now.
I myself have personally wanted to use an online service which claimed to be free, and the sign-up deterred me so I just gave a wrong email address. If it's a once-off action on behalf of the user (for example converting a file), users are lazy and even something like giving their email deters them.

I am happy to solve this issue with you, but I would need to get more details, following which we could have a short call to discuss the conclusions.
Good luck