I agree with Phil that it probably isn't a TFS issue.
Step 1 with debugging that for me would be to grab a different developer and have them try what I was doing. If it works for them, it is a problem with my setup. If it doesn't work for them, then something is configured funny.
Alternately, any good version control system will have the ability to check out an older version of the code. Grab an older version that is known-good and see if you can deploy. If you can, go up a version and repeat until you get to the version that is bad. Then compare the differences between those 2 versions.
My guess is there is a configuration change that happened at some point or possibly you don't have permissions to the deployment folder location hence the error.
That being said, I never use the deploy option from SSIS. I take my DTSX and push it into the SSIS catalog manually. It is very rare that I am changing more than 1 or 2 DTSX's at a time, so using deploy feels like overkill.