In a U-turn on a previous rejection, the group said it recommends shareholders accept the 11.4p-a-share offer tabled in April, which remains open for acceptance, after a "poor" first quarter has cast doubt over its full-year profit out-turn and led to concerns over the longer term financial position of the group.
Bonmarche warned that its auditor had said it may include a reference to the "uncertainty with regard to going concern" in full-year accounts due to the trading troubles and without any sign of improvement in revenues.
The group said first-quarter trading had been hit by a tough wider clothing market as well as the recent wet weather. It cautioned that while it is possible that full-year profits may hit forecasts, there is a "significant degree of uncertainty attached to this".
Bonmarche said: "Whilst the board's view remains that the offer does not adequately reflect the potential longer-term value of the business, the increase in uncertainty that has developed reflecting the trading and financial position of the business during the first quarter of the financial year makes the certainty represented by the offer potentially more attractive in the short term."
It said it now believes the offer is "fair and reasonable" and that Day would be a "successful long term owner", although he has not yet agreed to the board's request to discuss his future plans for Bonmarche.
Day - who is behind The Edinburgh Woollen Mill Group and owns a number of other retailers such as Peacocks, Jane Norman and Austin Read - acquired more than half of the company's shares in April through holding company Spectre, triggering a mandatory takeover bid.
Spectre said at the time that it would undertake a profitability assessment on Bonmarche's estate of more than 300 stores and shutter under-performing sites or reduce costs by cutting the number of staff or seeking a lower rent.
The bid came after Bonmarche issued its third profit warning in just six months in March.