Just five days before the series begins, the tourists were forced to play without two of their members of the first choice XI, sparking concerns ahead of Tuesday.
Wood, the standout quick during a dismal Ashes campaign, has yet to play any part against a CWI President's XI and did not turn up to play on day three having felt unwell during the past 48 hours.
As for Robinson, he was forced to leave the field after sustaining a lower back injury midway during his first spell. The Sussex seamer took the only wicket of the session when he had Devon Thomas lbw with one that nipped back in on a docile pitch.
It's something England could have done without having left out James Anderson and Stuart Broad for the series.
Uncapped duo Saqib Mahmood and Matt Fisher - who had not been due to feature in the match - were both called into action to replace them in an unexpected chance to prove their credentials in soporific conditions.
Both acquitted themselves steadily without being able to part Keacy Carty (44no) and Raymon Reifer (42no).
Responding to England's 466 for six declared, an innings which featured four half-centuries and a Jonny Bairstow hundred, the home side reached 133 for three at lunch.
With precious little in it for the bowlers, Robinson did well to jag one back into Thomas' pads early on but things were about to take a turn for the worse for the Sussex man. After sending down the third ball of his fourth over he walked gingerly from the pitch seeking treatment.
It was later confirmed that he had a sore back, recalling the back spasm he suffered during the fifth Ashes Test, and was being monitored.
Chris Woakes, the senior seamer on tour, went to the break wicketless from 14 overs.