A few doubts had been raised about how long Veh would last after he announced that he will not be renewing his contract when it expires at the end of June.
The club were believed to be considering bringing forward their planned change at the helm, but as the Eagles prepare to face Borussia Monchengladbach on Wednesday, that no longer seems on the agenda.
"The coach has got everything under control," said Frankfurt's director of sport Bruno Hubner, who says there is no rush for them to find a replacement.
"We've got to get it right. Veh has our full faith right up to the end of the season.
"We have a clear philosophy at the club, upon which we select the players we want to sign, and we apply the same criteria to our search for a new coach."
Like at the weekend, Veh is likely to have to get by without Alexander Meier, yet considering the five goals they put past Nurnberg at the weekend, that should no longer be of too much concern.
Losing Pirmin Schwegler to the flu is more of a worry, though, and Veh says he does not expect him to be fit for the weekend either.
"He's taking antibiotics and is a doubt even to face Wolfsburg on Saturday," said the Frankfurt coach.
Gladbach will be looking to extend their recent upturn in form when they travel to Frankfurt with the chance to move into the top four.
"It's definitely not going to be easy, but of course we're hopeful that we can get another win to go with our last two," said Christoph Kramer on his club's official website.
"Eintracht have an incredibly strong attack. Apart from Alexander Madlung and Marco Russ - and even they score regularly - all of their team are attack-minded."