England were allowed to replace the all-rounder, who had taken no part in Friday's play against Border, with Martin McCague, whose enthusiasm was quickly dissipated by a wicket that belonged in the adjacent graveyard.
It led to another soporific day's play with just 216 runs being scored off 101 overs. It ended with Border, at 125 for 5, still 195 runs behind an England first-innings total heavily dependent on Steve Rhodes' six-and-a-half hour century.
Cork is not expected back and the absence of his lower-order batting could give Mark Lathwell an unexpected recall as a sixth batsman. Despite Rhodes's well-constructed hundred, there is concern over a line-up of Rhodes, Robert Croft and Mark Ilott batting six, seven and eight.
If Lathwell does play it is likely to be as an opener, as Adrian Dale - who would bat three if John Crawley was promoted - would be required as the third seamer since both spinners are expected to play.
Both Croft and Peter Such will get plenty of bowling in this match as the pitch, which negates pace completely, merely dulls spin bowling. It was Croft who mercifully dismissed the Border opener Andrew Lawson after a turgid innings.
Having recovered from the shock of finding the Welsh flag in the swimming pool on Friday night - his team-mates having tired of his joy at Wales's rugby revival - Croft bowled a spell of 17 overs for 14 runs with the wicket of Lawson, well caught by a tumbling Ilott at mid-on.
Lawson, allegedly one of South Africa's most promising young batsmen, had batted close to three hours for 23 as play, on a blustery day that was more Scarborough than South Africa, crawled along at two runs an over. Four overs later, as England's fielding reached rare heights, Rhodes ran out Bradley Osbourne from the length of the pitch then Hugh Morris took a sharp diving catch to dismiss Piet Botha during a testing spell from Ilott.
England had resumed at 229 for 6 with Rhodes 59 not out from more than four hours batting. Driving the spinners through cover and tucking the quicker bowlers either side of the wicket, he reached 99 before, in his haste to reach his sixth first-class hundred, he ran out Ilott attempting a risky single.
It was four nervous overs later - especially for the non- striker McCague - when he lapped Ian Howell's off-spin for a well-deserved first century in four A and one B tour with England. It was his fifth first- class hundred in two years - an increase, said Rhodes, that is due to four-day cricket's greater opportunities.
With Croft already departed, Rhodes had a brief slog, being caught at mid-on, and
McCague, having hit Howell for six, was caught at long-off attempting a repeat.
It was another tiny crowd with the players outnumbering the spectators, who included a large crab scuttling among the seats of this seaside ground. The rest of the local sports fans were presumably engaged on more entertaining matters such as watching Aston Villa and Chelsea live on television.
(Second day of four; England A won toss)
ENGLAND A - First Innings
(Overnight: 229 for 6)
S J Rhodes c Stonier b Botha 108 R D B Croft b Howell 29 M C Ilott run out 0 M J McCague c Bauermeister b Howell 13 P M Such not out 2 Extras (b2 lb3 w4 nb1) 10 Total 320
Fall (cont): 7-285 8-296 9-308.
Bowling: Fourie 21-2-84-2; Badenhorst 27- 3-92-2; Botha 24-10-36-1; Howell 39-21-49-3; Strydom 2-0-5-0; Bauermeister 19-5-31-0; Cronje 7-3-18-0.
BORDER - First Innings
A G Lawson c Ilott b Croft 23 B M Osborne run out 50 P J Botha c Morris b Ilott 16 P C Strydom not out 16 F J Cronje not out 3 Extras (b1 lb3 w1 nb4) 9 Total (for 4) 125
Fall: 1-12 2-88 3-91 4-114.
To bat: *S J Palframan, K Bauermeister, I L Howell, B C Fourie, A Badenhorst.
Bowling (to date): McCague 8-2-16-0; Ilott 10-3-23-1; Taylor 13-3-29-1; Croft 23-8-31-1; Such 12-5-22-0.
Umpires: K Liebenberg and E Baillie.