The charity, which offered residential treatment at the facility until 2017 and continued other therapy there since, revealed it would list the building for sale from Monday as it looks for a new location.
However, it will remain open until the move is complete, having also been used as a vaccination centre during the coronavirus pandemic.
Councillor Janke described the sale as a "punch in the guts for veterans in the region".
"I am deeply saddened and frustrated to learn that Audley Court, as of June 14, will be put up for sale by Combat Stress," he said.
"As previously reiterated, respite care is vital in helping veterans deal with PTSD and in some cases, steering them away from suicide.
"To also learn that an alternative premises has yet to be found and no mention of a reintroduction of respite service is extremely disappointing to say the least.
"I understand that this news will be a punch in the guts for veterans in the region and those who have come forward in support of retaining the building for such a special community, but I want to assure you that possibilities for trying to keep this building in place so it may continue providing the care it was designed for are still being explored.
"This is not yet the end of the line of this particular battle and I hope to bring more positive news going forward.
"We are still fighting your corner and hope for a favourable outcome for veterans suffering with PTSD."
Combat Stress said the premises at Audley Court were no longer suitable for its service and that it was working with veterans to find a more cost-effective location within the central region of the country.
Interim chief executive officer of Combat Stress, Jeff Harrison, added that the move would not affect the number of people receiving support in the Shropshire and Telford & Wrekin areas.