Never Underdressed was launched in May 2013 to target women with luxury fashion content. Carrie Tyler, a former digital director of Elle, edits it.
It will cease publication this week and ShortList Media has entered into consultation with its 14 editorial members of staff for the website.
Soutar said Never Underdressed had met its advertising targets for its first year.
He said: "What became clear as we looked ahead to next year and beyond was that the team had established a beautifully crafted, high-end product but the ability to scale it was not there.
"The decision to close has not been taken lightly. We carried out an extensive examination of issues facing the site, but could not see a viable future for the luxury product we've all been so proud of since its inception.
"Rather than reposition Never Underdressed into something unrecognisable we are acting now to stem its losses."
ShortList Media has several other digital publications, including Emerald Street and Mr Hyde, the online newsletter brands for its Stylist and ShortList brands respectively.
Soutar said: "ShortList Media is a launch-driven business and like any company that tries to innovate, not everything we do will succeed.
"The rest of our portfolio is having a record-breaking year and our focus will remain to invest in and build the power and reach of our existing brands, and to continue to seek out market gaps to explore with exciting new products.
"There are lessons to be learned from Never Underdressed and we will certainly reflect on how we can use this experience to build our launch capability in future."
When it launched, Never Underdressed was described as a "digital, multi-platform, glossy fashion and beauty title that combines the high-gloss production values of monthly fashion magazines with the hourly speed and immediacy of the web".