After the half-hour mark, Orient enjoyed their best chances of the first half when Jay Simpson's header from close range was blocked by the besieged Dons defence, before Shane Lowry brought another stop out of Martin.
Despite the home side's opportunities, the visitors almost took the lead after the break when Jordan Spence fired a shot inches wide of Gary Woods's left post.
However, Orient continued to look the more likely as Simpson's effort was kept out by Martin before Henderson squandered another chance.
Simpson then missed again with a free kick, but Orient were nearly caught out when Kyle McFadzean headed a corner over the crossbar late on.
Samir Carruthers then fired another warning shot as his free kick on 88 minutes came close to beating Woods, and the Dons' hopes of snatching a late victory were boosted when Mathieu Baudry was sent off for a second bookable offence, but the O's held on for a well-earned draw.