So Theresa May is facing a vote of no confidence in her leadership of the Conservative party today. It's unclear if she will be ousted or not.
What happens if the vote fails?
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Under current Conservative Party rules, she remains leader, and cannot be subject to a party confidence vote for another year.
Being a party matter, none of this affects any parliamentary vote of no confidence which might take place.
Source: BBC News.
See also: Leadership Elections in the Conservative Party, House of Commons briefing paper 01366, July 2016.
The (probably) failing attempt of vote of no confidence mostly shows how divided even the own conservative party is despite representing the PM.
If the vote fails, Mrs. May has definitely a stronger position than without such a vote even taking place. She would know there is no clear majority against her course and likely there is also no clear majority in the parliament. The fact that a no-confidence vote is even instigated would normally question the position of the PM. However, in May's current situation with criticism from all sides ever since she took office, a failed vote paradoxically supports her position (even if it is only the fact that there might be no persuasive alternative). Therefore, I believe once the vote has failed, May gained more time for her efforts either to renegotiate parts of the deal (which I doubt will happen in a substantial manner) or to set a new date for the vote on the deal.
If the vote succeeds, May will step down and probably a more pronounced Brexit supporter will take her place. I doubt however that neither Johnson nor Rees-Mogg would get the position.
To sum up, a failed vote would indirectly support the current position of May while a successful vote would end her period as PM.