How likely are judges to grant vexatious litigant cases?

Not a vex lit yet but I would bring his actions to the courts attention and ask for sanctions.

It depends on whether the motions are filed for new reasons or based on new facts. If he is improperly filing essentially the same motion repeatedly, then you may be able to successfully argue that he is a vexatious litigant under California Code of Civil Procedure, Section 391(b)(3): "(b) "Vexatious litigant" means a person who does any of the following: . . . (3) In any litigation while acting in propria persona, repeatedly files unmeritorious motions, pleadings, or other papers, conducts unnecessary discovery, or engages in other tactics that are frivolous or solely intended to cause unnecessary delay." Whether your potential motion to declare him a vexatious litigant will be granted also depends on the judge. Has the judge been patient or frustrated with these motions to reduce child support? Another option is to file a motion for sanctions under California Code of Civil Procedure, Section 128.7, which can also provide relief by striking frivolous motions.

this may help you: As used in this title, the following terms have the following meanings: (a) "Litigation" means any civil action or proceeding, commenced, maintained or pending in any state or federal court. (b) "Vexatious litigant" means a person who does any of the following: (1) In the immediately preceding seven-year period has commenced, prosecuted, or maintained in propria persona at least five litigations other than in a small claims court that have been (i) finally determined adversely to the person or (ii) unjustifiably permitted to remain pending at least two years without having been brought to trial or hearing. (2) After a litigation has been finally determined against the person, repeatedly relitigates or attempts to relitigate, in propria persona, either (i) the validity of the determination against the same defendant or defendants as to whom the litigation was finally determined or (ii) the cause of action, claim, controversy, or any of the issues of fact or law, determined or concluded by the final determination against the same defendant or defendants as to whom the litigation was finally determined. (3) In any litigation while acting in propria persona, repeatedly files unmeritorious motions, pleadings, or other papers, conducts unnecessary discovery, or engages in other tactics that are frivolous or solely intended to cause unnecessary delay. (4) Has previously been declared to be a vexatious litigant by any state or federal court of record in any action or proceeding based upon the same or substantially similar facts, transaction, or occurrence. (c) "Security" means an undertaking to assure payment, to the party for whose benefit the undertaking is required to be furnished, of the party's reasonable expenses, including attorney's fees and not limited to taxable costs, incurred in or in connection with a litigation instituted, caused to be instituted, or maintained or caused to be maintained by a vexatious litigant. (d) "Plaintiff" means the person who commences, institutes or maintains a litigation or causes it to be commenced, instituted or maintained, including an attorney at law acting in propria persona. (e) "Defendant" means a person (including corporation, association, partnership and firm or governmental entity) against whom a litigation is brought or maintained or sought to be brought or maintained. 391.1. In any litigation pending in any court of this state, at any time until final judgment is entered, a defendant may move the court, upon notice and hearing, for an order requiring the plaintiff to furnish security or for an order dismissing the litigation pursuant to subdivision (b) of Section 391.3. The motion for an order requiring the plaintiff to furnish security shall be based upon the ground, and supported by a showing, that the plaintiff is a vexatious litigant and that there is not a reasonable probability that he or she will prevail in the litigation against the moving defendant. - See more at: http://codes.lp.findlaw.com/cacode/CCP/3/2/3A/s391#sthash.gE87dTQr.dpuf

I would absolutely raise this issue with the Court and request sanctions. I'm nor sure how quick Court's are to label someone vexatious, but the Judge should be made aware that these failed motions evidence your belief that your ex is simply trying to harass you.