[NOTE:  The following cases have not been checked.  Be certain that you check every case you use!]

When you do a counterclaim does that mean their claim is no longer active?

Yes.  They temporarily lose jurisdiction because in the first cause of action the question of jurisdiction is the issue.  Once jurisdiction is challenged, jurisdiction cannot be ‘assumed’, it must be proven to exist. They must prove they have jurisdiction before they may proceed.

============================ ============================

"However late this objection has been made, or may be made in any cause, in an inferior or appellate court of the United States, it must be considered and decided, before any court can move one further step in the cause; as any movement is necessarily the exercise of jurisdiction. Jurisdiction is the power to hear and determine the subject matter in controversy between parties to a suit, to adjudicate or exercise any judicial power over them; the question is, whether on the case before a court, their action is judicial or extra-judicial; with or without the authority of law, to render a judgment or decree upon the rights of the litigant parties. If the law confers the power to render a judgment or decree, then the court has jurisdiction; what shall be adjudged or decreed between the parties, and with which is the right of the case, is judicial action, by hearing and determining it. 6 Peters, 709; 4 Russell, 415; 3 Peters, 203-7"  
Cited by STATE OF RHODE ISLAND v. COM. OF MASSACHUSETTS, 37 U.S. 657, 718 (1838) 
This cite has been verified.

If they proceed without proving their jurisdiction to the counterclaiming court, then the proceedings from that point onward are void.

"Where a court has jurisdiction, it has a right to decide any question which occurs in the cause, and whether its decision be correct or otherwise, its judgments, until reversed, are regarded as binding in every other court. But if it act without authority, its judgments and orders are regarded as nullities. They are not voidable, but simply void, and form no bar to a remedy sought in opposition to them, even prior to a reversal. They constitute no justification, and all persons concerned in executing such judgments or sentences are considered in law as trespassers."
Elliott v Peirsol, 1 Pet. 328, 340, 26 U.S. 328, 340, 7L.Ed. 164 (1828)
This cite has been verified.

However, they are law breakers, and they typically attempt to proceed anyway.  So, sometimes you have to deal with them with a counterclaim, writ of error, or contempt.

"No officer can acquire jurisdiction by deciding that he has it. In all such cases, every officer, whether judicial or ministerial, decides at his peril.”"  
John Middleton v. F.F. Low, Governor of California (1866), 30 Cal. 596, 607
This cite has been verified.

"But where the question upon which the jurisdiction depends is one of law purely the jurisdiction over the subject matter is always open to collateral inquiry ...”  
Grannis v. Superior Court, 146 Cal. 245 [79 P. 891, 106 Am.St.Rep. 23] 
Not verified

QUALIBET JURISDICTIO CANCELLOS SUOS HABET. Jenk. Cent. 137. 
"Every jurisdiction has its own bounds".
Not verified

"Subject matter jurisdiction, however, is determined from the pleadings, and once a proper charge is filed in circuit court, that court may exercise jurisdiction over that subject matter." Simpson v. State, 310 Ark. 493, 499, 837 S.W.2d 475 (1992).
This cite has been verified.

"Jurisdiction of the person and of the subject matter is not alone conclusive [and] the jurisdiction of the court to make or render the order or judgment" depends upon due observance of the constitutional rights of the accused. 
25 Am.Jur., Habeas Corpus, sec. 27, p. 161. 
See also Palmer v. Ashe, [342 U.S. 134, 72 S.Ct. 191, 96 L.Ed. 154].
Not verified

"Jurisdiction cannot be assumed by a district court nor conferred by agreement of parties, but it is incumbent upon plaintiff to allege in clear terms, the necessary facts showing jurisdiction which must be proved by convincing evidence." 
Harris v. American Legion, 162 F. Supp. 700. 
[See also McNutt v.General Motors Acceptance, 56 S. Ct. 780.] [Italics added]. 
Not verified

“Proceedings in a court are legally void where there is an absence of jurisdiction.” 
Scott v. McNeal 154 US 34; Re: Bonner, 151 US 242.;
Not verified

 “...federal jurisdiction cannot be assumed, but must be clearly shown”. 
Brooks v. Yawkey,  200 F. 2d 633 
Not verified

Get the Judges OATH OF Office and file a Motion to 
Dismiss for Lack of Territorial Jurisdiction. 
Not verified

“No sanction can be imposed absent proof of jurisdiction”. 
Stanard v. Olesen,  74 S. Ct. 768 
Not verified

“The law requires proof of jurisdiction to appear on the record of the administrative agency and all administrative proceedings”.  
Hagans v. Lavine,  415 U.S. 533 
Not verified

“If any tribunal finds absence of proof of jurisdiction over person and subject matter, the case must be dismissed”. Louisville Rail Road v. Motley,  211 U.S. 149,  29 S.Ct. 42 
Not verified

“Jurisdiction is essential to give validity to the determination of administrative agencies and where jurisdictional requirements are not satisfied, the action of the agency is a nullity...” City Street Improvement Co. v. Pearson,  181 C. 640,  185 P. 962, 
Not verified

BOGUS CITES

There are a lot of bogus cites on the Internet.
The following cites are bogus and must not be used:

“Once challenged, jurisdiction cannot be ‘assumed’ it must be proved to exist”. 
Stuck v Medical Eaminers, 94 Ca.2d 751,  211 P. 2s 389 

“Jurisdiction once challenged cannot be assumed and must be decided”. 
Main v. Thiboutot,  100 S.Ct. 2502