The Irishman started the day in fifth place on General Classification just 1’12” down on race leader Chris Froome but disaster struck inside the final 20 kilometres.
First, strong winds from the side forced an acceleration in the pace as Team Sky rode as hard as they could to keep Froome in the front and out of any danger.
It’s a common strategy employed by teams also willing to thin down the main field and is often done when teams sense others are momentarily lapsing, or badly-positioned.
Martin was further back the peloton at the time of the sudden surge and he became isolated when Sky’s searing pace forced a small group to break off the front.
And with most of the main contenders in there like Romain Bardet, Fabio Aru and Rigobert Uran, the pace slowed down behind.
With his team-mates even further back trying to ensure sprinter Marcel Kittel made it inside the time limit, Martin started to lose time as only Jack Bauer and Gianluca Brambilla were in his group to commence a chase.
It didn’t help their cause either that they were without Matteo Trentin and Philippe Gilbert who abandoned with illness.
Try as they might, the men in blue never tacked onto the rear of the peloton and Martin crossed the line 51 seconds down on the front group containing all of the other GC men, including Froome.
“I was a bit sick on Monday and then some of the other guys have been sick as well,” said Martin afterwards.
“(Zdenek) Stybar has been sick and (Julian) Vermote has been sick. The team’s really struggling.
“We put on a brave face yesterday hoping that they would be able to protect me but in the end I only had Gianluca and Jack.
“They did an incredible job all day. Jack was killing it at the end.
“I wasn’t in a bad position, but it was probably me who didn’t have the legs or the power in the wind. It happens. It’s unfortunate.
“We worked so hard to be in this position but it’s not over,” he added.
Fellow Irishman Nicolas Roche (BMC Racing) did well to make the split of just over 20 riders, though he was tailed off it in the last kilometre having worked for team-mate Greg Van Avermaet.
Martin would finish 31st and has now been overtaken in the general classification by Mikel Landa (Team Sky) and Simon Yates (Orica-Scott).
“I can’t say it’s the best situation for us, but the team is upbeat and optimistic about our chances now that the race is heading into the Alps for two days,” continued Martin.
The stage was won by Australian Michael Matthews, his Team Sunweb outfit having played a blinder in keeping Kittel off the back once he was dropped.
Matthews finished off the job with a very narrow victory over Edvald Boasson Hagen (Dimension Data) and John Degenkolb (Trek-Segafredo).
Froome still leads overall with just five stages remaining, the first of which is today’s 183-kilometre stage from La Mure to Serre Chevalier.
Martin will now need to really go on the offensive if he is to claw his 2’03” deficit back on Froome and with two Hors Categorie climbs as well as two more categorised ascents today, he’s unlikely to waste any time in trying to get up the road.