The third seeds beat Australians Lleyton Hewitt and Chris Guccione to reach the title match but could not overcome France's Edouard Roger-Vasselin and Holland's Igor Sijsling on Sunday, losing 7-6 (8/6) 6-3.
It was a second final this season for the Marray-Fleming combination, who were also runners-up in Eastbourne last month.
Sheffield's Marray and Linlithgow's Fleming pushed the first set to a tie-break, despite Roger-Vasselin and Sijsling looking the stronger team.
But once that slipped away, Roger-Vasselin and Sijsling took control with an early break in the second set that sufficed as the rest of the contest went with serve.
Fleming said on Twitter afterwards: "Tough loss today, opponents served rocks. Decent week though and no time to dwell as off to airport already heading for DC."
The duo will play in this week's Citi Open in Washington as they continue their preparation for next month's US Open.
Elswehere in North America on Sunday, there was good news for Brits James Ward and Johanna Konta as both picked up 'second tier' singles titles.
British number two Ward beat Australian James Duckworth 4-6 6-3 6-4 in Lexington to win the ATP Challenger Tour event in Kentucky, while Konta saw off compatriot Samantha Murray 6-3 6-1 to triumph in the ITF Pro Circuit tournament in Winnipeg.
Ward climbs back into the world's top 200 as a result of his win - he's up to 179th in the rankings.