The Sky Blues have now not won at the Ricoh Arena since early October even though they took the lead after only 36 seconds against shell-shocked Ipswich.
Danny Fox played the ball into the box from the left and Robbie Simpson's header fell neatly to Clinton Morrison. The big striker's initial shot was blocked by Ipswich defender Gareth McAuley but Morrison quickly rammed in the rebound from 12 yards.
The visitors recovered from the early setback with Kevin Lisbie and Jonathan Stead both having good chances before the equaliser arrived in the 12th minute.
Stead's flick-on bamboozled Coventry's defence and Lisbie collected the ball to drill home a strike from ten yards.
In an open game, Ipswich then enjoyed a spell of possession with Alan Quinn setting up Tommy Miller to try his luck from 22 yards and the same player created a chance for Lisbie but his close-range header was deflected over by Keiren Westwood.
The Sky Blues should have regained the lead five minutes before the break when Freddy Eastwood played a one-two with Michael Mifsud before firing an angled shot against the bar.
Ipswich started the second half brightly with Lisbie and Stead again testing Westwood but it was Coventry who retook the lead in the 56th minute.
A long pass from Fox reached Eastwood and the striker shrugged off an Ipswich defender to beat Richard Wright with a near-post shot.
The Tractor Boys again showed their mental strength by drawing level in the 65th minute when Lisbie took advantage of a defensive lapse to send a lob over Westwood from 12 yards.
Ipswich nearly handed the Sky Blues the lead for a third time when McAuley sent a shot crashing against his own bar.
But the visitors could have won the match in the 89th minute when Westwood saved a 25-yard shot from Darren Ambrose and the follow-up effort from fellow substitute Jon Walters.