I found a bit of information about the Nielsen ratings for the show at tvobscurities.com:
The pilot for Mrs. Columbo did well, ranking 18th [most watched show of the week], but when the series moved to its regular Thursday time slot it slipped to 45th
The source for this is apparently The TV Column by John Carmody in the 7th March 1979 issue of the Washington Post, though I can't find any archives of the paper to back this up.
In addition to changing timeslots, there were issues with the production, as documented on Kate Mulgrew's website:
The third episode was pulled and replaced with an old “Quincy” show when it was apparent that the show simply would not be finished. The cast and crew got a breather, but remained behind schedule.
So already it sounds like the show was being set up to fail. This information is backed up at the Episode Guide section of the website:
Monday February 26th, 1979: 2 Hour pilot "Word Games" broadcast
Thursday March 1st, 1979: "Murder Is A Parlor Game" broadcast
Thursday March 15th, 1979: "A Riddle For Puppets" broadcast
So instead of the episode on March 8th, they got an announcement from NBC:
On March 8, after “Mrs. Columbo” had been on the air for exactly one week, NBC announced in a carefully worded statement that the show was being “dropped” from the schedule. Dropped, not canceled. NBC promptly announced six new shows, also in “limited” runs—sort of replacements for the replacements.
Later on in the tvobscurities article they mention fallouts between the producers of the original Columbo and Mrs. Columbo, so it sounds like they had completely different staff because of it, which couldn't have helped:
In early 1979, Fred Silverman had the idea to feature “Lt. Columbo’s wife” (often talked about by Columbo, but never seen) in her own mystery series, but creator/producers Richard Levinson and William Link wanted no part it, as they’d previously made a pact with Peter Falk “never to show Mrs. Columbo”. Silverman bypassed them, and got another Universal producer, James McAdams, then David Levinson to film the series. In an effort to draw more attention to Kate Mulgrew’s character, the series was quickly retitled Kate Columbo. Yet the series continued to slip in the ratings. Silverman, however, renewed it for the fall, finally deciding to sever all ties to Columbo, altering Kate’s last name to “Callahan”, and again retitling it Kate Loves A Mystery It finally went off the air for good at the end of the year.
As shows such as Firefly have proven, even if a show is critically acclaimed, messing with the broadcast schedule can irreparably damage the show's potential, especially in 1979 when video recorders were rare and DVR was a dream.