Draws with Arsenal and Watford and defeats by Hull City, Crystal Palace and Everton have seen Bournemouth drop from ninth place at the end of 2016 to six points above the relegation zone, but Mostyn said Howe's position was not under threat.
"Eddie is our manager and will continue to be our manager for the foreseeable future," the chairman told the BBC.
"It is always a concern when you are not winning games. Over the last three or four years the team have always had a poor run of form in January and February.
"I am totally convinced we will get back to winning ways. February presents us with a very difficult programme, but the Premier League is topsy-turvy."
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Bournemouth were knocked out of the FA Cup by third-tier Millwall in January and had a quiet transfer window in which they lost defender Nathan Ake to Chelsea, after the league leaders cut short the 21-year-old's loan spell.
"January was extremely frustrating," Mostyn added. "The most frustrating thing of all is that we didn't get anything over the line. But it was not for the lack of trying.
"Chelsea calling Nathan back was a blow that was hard to take, especially when the manager lavishes praise on the club for the progress he has made and then he is likely to sit in the stand."
(Writing by Simon Jennings in Bengaluru; Editing by Hugh Lawson)
