Even if Stark sued the government and won, the most he could have received is reasonable compensation for his costs and/or damages. Under US patent law, he can't stop the US government from using a patented product if it so chooses.
It is also possible Stark had not patented some of the suit components. In order to receive a patent, you must make the details of your invention public. The invention could then be copied, for example by supervillains who do not care about being sued for patent infringement. Instead, Stark might effectively be keeping the suit as a trade secret. In that case he would have even less protection against the government using the suit's technology.
(I Am Not A Lawyer, but a quick Google indicates the law is pretty clear on these points.)