And, as with the stalemates against Chelsea and Watford in previous weeks, this was another game that Hammers will have been disappointed not to have taken all three points from.
First half goals from Daryl McMahon and David Noble had put the hosts in control against a young Ipswich side, but a 73rd minute equaliser from left-back Lee Chaffey earned the visitors a point, meaning that Hammers have now drawn half of their 18 matches this season.
Coach Roger Cross was able to field a positive blend of experience and youth, a contrast best summed up by the appearance in midfield of youth academy coach Kevin Keen alongside one of his schoolboy protégés, 15-year-old Mark Noble.
Christian Dailly continued in his temporary new role as a striker, partnered by his Scottish international team-mate Don Hutchison, while Sebastien Schemmel, Gary Breen and Scott Minto added seniority to the defence and former Arsenal midfielder Noble returned from injury to captain the side.
In a lively and end-to-end first half, it was Ipswich who should have taken the lead on 22 minutes, when striker Sam Morrow found himself unmarked just six yards out but shot straight at Raimond Van der Gouw, who gratefully clutched the ball to his chest.
Just two minutes later, the visitors were made to pay as Hammers opened the scoring with their first real chance of the game. A flowing move in midfield ended with Schemmel sending over a cross that was missed by an Ipswich defender at the far post and McMahon fired a first time shot past goalkeeper Pullen from 12 yards out.
However, Ipswich replied almost immediately and it was Morrow who turned the tables of embarrassment on Van Der Gouw, as his seemingly harmless 25-yard effort slipped from the grasp of the Hammers keeper and bounced into the net.
That lifted Town, who came close to taking the lead moments later when Abidallah's stinging 20-yard shot was well saved by Van der Gouw.
However, Hammers finished the half in impressive fashion. Hutchison had a goalbound volley blocked by two defenders on the line, while David Noble curled a shot over the bar from Schemmel's clever cut-back.
On the stroke of half-time, it was that same combination that teamed up to restore the hosts advantage. Another neat move saw Schemmel released again and his excellent cross was only cleared to the edge of the penalty area, where Noble was waiting to measure a controlled volley that found the bottom corner.
The second half settled down into a slower pace as Hammers attempted to protect their lead with possession football, although Dailly and McMahon both saw efforts deflected wide and Hutchison almost converted with a left-foot volley at the near post.
There appeared to be no danger as the game moved into its closing stages but, with 17 minutes remaining, a double injury blow proved vital. With the ball out of play for an Ipswich corner, Schemmel and Breen were forced off after collecting hamstring strains, leading to a defensive reshuffle that saw Dailly drop to left-back and Minto move across to an unfamiliar right-back role.
With the team still re-organising as the corner-kick was floated in, the ball wasn't cleared properly and Chaffey poked home the loose ball from six yards out.
David Noble sent a 25-yard free-kick just inches wide of the target moments later, but Ipswich held on for the draw and followers of the Hammers' second string were left to reflect on yet another share of the spoils at Dagenham and Redbridge.
Hammers: Van der Gouw, Schemmel (Pearson 73), Minto, Breen (Ward 73), Delaney, Keen, M Noble (M Cole 77), D Noble, McMahon, Dailly, Hutchison. Subs unused: A Ferdinand, Forde, Lumsden, Tattam.