Sterling has weakened more than 1pc this month as cross-party Brexit talks have yielded little and left May vulnerable to a leadership challenge.
She will set out a timetable for her departure in early June after the latest attempt to get her Brexit deal approved by parliament, but could face a confidence vote if the deal is voted down.
The prospect of May's demise is weighing on the pound because some investors think it could push Britain in the direction of a disorderly no-deal Brexit.
"What we're seeing is the market pricing in a higher probability of an exit without a deal," Adam Cole, chief currency strategist at RBC Capital Markets, said, noting the growing risk that the bill would fail to pass and May depart before parliament goes into recess in late-July.
"It looks increasingly likely she will be replaced by a pro-Brexit PM with no election, and that automatically increases the chances of a no-deal Brexit."
Sterling was down for the ninth straight session, touching a three-month low of $1.2794 and slipping 0.2pc against the euro to 87.4 pence, the lowest since February 19 .
May plans to put to her thrice-rejected Brexit agreement to parliamentary vote but Eurosceptics in her party and its Northern Irish allies, as well as opposition Labour lawmakers, are expected to reject it.
Boris Johnson, Britain's former foreign minister and a prominent campaigner to leave the EU, said on Thursday he will be standing as a candidate to replace May as Conservative leader, the BBC reported.
Britain's deadline for leaving the EU is Oct. 31.
May's failure to reach a compromise on the Brexit deal with Labour has also seen one-month implied sterling volatility rise to a five-week high.
The currency is also being undermined by the global risk-off mood, with tariff tensions between China and the United States threatening to degenerate into a full-scale trade war.