Sterling sank to an 11-month low on Monday after Britain's trade minister Liam Fox suggested the UK could leave the EU in March without a deal in place to ensure future relations with the bloc, its biggest trading partner.
The pound has fallen more than eight percent since April and with the government yet to agree a divorce deal with Brussels, currency traders are growing edgy about its outlook.
A lack of Brexit headlines and a pause in a rally by the dollar on Tuesday brought some respite for the currency, however analysts said that would likely only be temporary.
"The more we hear the phrase 'no-deal Brexit', the more likely the pound will be kept under the cosh," said David Madden, a market analyst at CMC.
"The British side might give off the impression they would be content without a deal in order to force Brussels's hand the pound could be in for a rocky ride in the near-term."
Sterling edged up 0.2 percent to $1.2973, away from Monday's trough of $1.2920, its lowest since July 19.
It remained broadly flat against a resurgent euro at 89.35 pence.
A stronger-than-expected reading of Britain's second-quarter growth data on Friday could lift the pound further but even a rebounding economy will struggle to reverse the pound's fortunes so long as a cliff-edge Brexit remains on the horizon, analysts say.
"GBP-bulls who are waiting for the data on Friday are having to endure quite a lot of pain," said analysts at Commerzbank in a note.
"How positive can the data - that only ever describes the past - actually become to be able to cover up the risks the UK economy is facing?"
If Britain leaves the EU without a transition agreement, it would revert to trading under World Trade Organization rules.
Most economists think that would cause serious harm to the world's fifth largest economy as trade with the EU, Britain's biggest market, would become subject to tariffs.
Supporters of Brexit say there may be some short-term pain for Britain's $2.9 trillion economy, but that long-term it will prosper when cut free from the EU and able to strike trade deals with faster-growing countries and regions elsewhere.