Mark Adderley was at the National Trust for Scotland for only 19 months before his sudden exit last week. A press statement from chairwoman Shonaig Macpherson said it was an "appropriate time" to seek new leadership at the trust.
But the charity, the largest membership group in Scotland, is hampered by a deficit of £800,000 and is in the middle of a three-year restructuring to improve finances.
The trust insisted Adderley had not been sacked from his post and said there were no plans to sell any its 129 properties.
Alan Denney, national secretary for Prospect union, said problems apparently stemmed from a "difference of opinion" between Adderley and the board.
Meanwhile, visitor numbers at Dawyck Botanic Garden in the Scottish Borders have risen by more than 72 per cent since the opening of a new visitor centre in May.