The Dundonian, joint second at halfway, believes he is still in with a chance of landing his first European Challenge Tour title since 2010 after adding a level-par 71 to his previous rounds of 68 and 67.
Murray is three behind joint leaders Jordi Garcia Pinto (68) and Tim Sluiter (69), who are on 10-under 203. He is tied for third alongside American Brooks Koepka (68). Three other Scots are in the top nine in Nairobi, and within five shots of the lead.
"I played pretty average today," said Murray, whose sole victory on the Challenge Tour came at the Scottish Hydro Challenge three years ago. "I just never really got going at all.
"I birdied the second and bogeyed the fourth with a wedge in my hand, which was poor. I hit a 6-iron in to 12ft at the fifth and holed that and then bogeyed the sixth with a 9-iron in my hand.
"I hit it stiff at the 10th from 112 yards which was nice but I didn't give myself any chances until the 15th. I thought I had holed my bunker shot but it took an awful bounce and went eight feet past and I missed the putt. It was more stupidity than anything else today. It's not done yet though. Hopefully I can go and shoot six or seven under tomorrow and maybe I'll have a chance."
David Law (71), Andrew McArthur (67) and Raymond Russell (72) are all on five-under and in a share of sixth place with England's Sam Hutsby.
In the Africa Open in East London, two South Africans lead the way on home turf after Darren Fichardt shot seven-under-par 65 to join Jaco Van Zyl (68) at the top of the standings on 15 under.
Fichardt fired four birdies and an eagle on the first eight holes, and his day would have been even better but for two bogeys, the second on the 17th. The pair, who are two shots clear, are vying to become the fourth successive South African to win this event.
They were among several players starting out early who were able to make the most of decent conditions before the wind picked up, leaving the frontrunners at halfway with a more difficult task.
The two Scots who survived the cut, David Drysdale and Chris Doak, were among a cluster of players 11 shots behind the lead in a tie for 40th after both shot 71s.