Facebook has denied that it is losing customers, saying it is "pleased" with growth.
Figures from Faceboook monitoring site Inside Facebook suggested that during May, Facebook lost six million users in the US and 100,000 in the UK.
But the social network, which does not usually comment on third party statistics, questioned how it arrived at this figure.
Other net measurement firms said they had seen growth over the same period.
"From time to time, we see stories about Facebook losing users in some regions. Some of these reports use data extracted from our advertising tool, which provides broad estimates on the reach of Facebook ads and isn't designed to be a source for tracking the overall growth of Facebook," the firm said in a statement.
"We are very pleased with our growth and with the way people are engaged with Facebook. More than 50% of our active users log on to Facebook in any given day," it added.
The figures from Inside Facebook claimed that 1.5 million Canadian users left the social network in May.
But overall it showed that Facebook was growing, to a total of 687 million users worldwide with many new customers coming from countries such as India, the Philippines and Indonesia.
Its figures on customer leakage do not appear to tally with those from net measurement firm comScore.
It told the BBC it had seen a 21% growth for US users on Facebook during May, while the UK gained 368,000 new recruits between February and May.
According to comScore, the average amount of time spent on the site was also up, from 21 minutes per day in December 2009 to 25 minutes per day by December 2010.
Measurement firm Nielsen said its figures also showed growth.
"There are months when figures dip but I'd be very cautious on calling a trend based on two months," said Nielsen spokesman Neil Beston.
The idea of Facebook fatigue, where users desert the social network after a certain period of time has long been talked about by experts but remains unproven.
"In developed countries such as the US and the UK Facebook penetration is hitting 50% and at that level it is inevitable that users will sign up who aren't frequent visitors," said Adrian Drury, lead analyst at research firm Ovum.