May has already warned MPs (Members of Parliament) that if her deal fails to get enough parliamentary support, a lengthy delay to the Brexit process might be necessary.
No date has yet been scheduled for the third so-called "meaningful" vote. However, the government motion states it must take place before March 20.
On Thursday, the House of Commons is due to vote on whether to ask the EU for permission to delay Brexit beyond 29 March.
It comes after U.K. lawmakers rejected the idea of leaving the bloc without a Withdrawal Agreement in place on March 29. Westminster also narrowly backed an amendment that rejected a no-deal Brexit in any circumstance.
The approved motion to block a no-deal Brexit — which refers to the so-called "cliff-edge" scenario where Britain leaves abruptly on March 29 with no 21-month transition period and is forced to revert to WTO trading rules — was not legally binding.
But, given the amendment passed, thanks to a large rebellion by members of May's own Conservative Party and cabinet, analysts at Citi said it "severely undermines" her authority and could potentially trigger another wave of ministerial resignations.
In January, May's proposed Withdrawal Agreement lost by a record majority of 230 votes when euroskeptic and pro-EU lawmakers voted against a deal they claimed was the worst of all worlds.
On Tuesday, the prime minister's Brexit deal suffered a second humiliating defeat as it was voted down by a majority of 149 votes.
Analysts at Citi questioned whether a third meaningful vote would be May's "last hope" to push through a close variant of her Brexit deal.
"If (a third meaningful vote) passes, the government would request an extension of Article 50 until 30 June to implement the deal. Alternatively, the motion suggests a longer extension would be necessary and EU elections would need to be held," analysts at Citi said in a research note published late Wednesday.
"Theresa May's hope might be that the prospect of a long extension gets the ERG and DUP to vote for the deal," they added, referring to the Northern Irish Democratic Unionist Party — which props up the government in Parliament — and a group of pro-Brexit lawmakers in the Conservative Party.
Meanwhile, Goldman Sachs believes there is an increased likelihood of May getting a similar version of her Brexit deal ratified in Parliament.
The U.S. investment bank estimated there is now a 60 percent chance of success for May's Withdrawal Agreement, up from 55 percent on Wednesday.
Goldman Sachs said it still sees a "considerable" chance Brexit will be reversed by means of a second referendum. The bank has set subjective odds at 35 percent.
It also reduced the probability of a no-deal Brexit to 5 percent, down from 10 percent.