Jeff:

I looked over your code and see a small problem.

A snippett of your code:

MOV R6, #8 

Extra_clocks: 
MOV R6, 6 
SETB P1.0 
CALL Time_Delay_Very_Short 
CLR P1.0 
CALL Time_Delay_Very_Short 
DJNZ R6, Extra_Clocks 

Needs to be changed to:

MOV R6, #6      ;;#8 wrong count

Extra_clocks: 
;; MOV R6, 6   this line is questionable 
SETB P1.0 
CALL Time_Delay_Very_Short 
CLR P1.0 
CALL Time_Delay_Very_Short 
DJNZ R6, Extra_Clocks 

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Also - Your control byte value indicates that you selected external clocking so make sure that you are not clocking too fast through the last two clocks of the control byte so the Tacq time from the MAX1112 data sheet is met.

Also - On the MAX1112 data sheet they indicate to make sure the total converion time does not exceed 1 ms to avoid excessive T/H droop. (See the Simple Software Interface section).
Good Luck
Mike Karas