I have a temporary restraining order against the abuser. Can his/her gun be taken away?
Possibly. As of October 1, 2016, Connecticut state law prohibits someone from getting a certificate to carry a pistol or revolver if there is an ex parte restraining order against him/her that was issued due to the use, attempted use or threatened use of physical force against another person.1 If s/he already has a certificate to carry a pistol or revolver, it will be revoked once an ex parte order is issued and s/he will be required to turn in his/her certificate to law enforcement within five days of receiving notice of the revocation.2
However, the Connecticut criminal laws (section 53a-217 and 53a-217c) that make it a crime to have any firearm or ammunition in one's possession only refer to restraining orders that were issued after notice and a hearing, not ex parte orders.3 Therefore, if the judge gave you an ex parte temporary restraining order (which means that no advance notice was given to the abuser), which is commonly done, it could still be legal for the abuser to possess certain types of firearms and ammunition.
1 C.G.S.A. § 29-36f(b)(6)
2 C.G.S.A. § 29-36i(a),(b)
3 C.G.S.A. §§ 53a-217(a); 53a-217c(a)