While 46% of the 1300 adult respondents surveyed by OnePoll said they had thought about leaving Facebook, or had already left, that number increased to more than 50% when focusing on the over-45s.
For the younger age groups, more than a third said they had considered ending their membership recently. Men also showed more negative sentiments, with more than 50% thinking about leaving the service, compared with 39% of women.
The survey comes as Inside Facebook, a company that tracks Facebook developments, claimed last week that almost 6m fewer people in the US used Facebook between May and June, while user numbers in the UK dropped by 100,000.
However, a spokeswoman for Facebook said it was 'very pleased' with its growth, adding that such stories often used data extracted from its advertising tool, which was not designed to accurately track overall growth.
Marketing's research also confirmed that privacy was an issue for all age groups, with 58% of respondents saying they were concerned about how Facebook used their personal information. The number rose to 65% for over-45s.
The under-35s were the most prolific users via mobile, with one-third saying it was their main point of access.