The AD&D second edition spell living link can be found in the Complete Book of Necromancers. It states the target of the spell receives no saving throw due to the fact the target does not know it is being targeted. However, one of my players cast this spell on a Mind Flayer which has Resistance to magic of 90%. I rolled the die and sure enough the spell failed… one unhappy player was the result! So should the Mind Flayer or other creatures with Magic Resistance be affected by this spell or not?
Magic Resistance always takes effect unless there is a specific reason why it should not (usually indicated in the spell).
AD&D DMG pg. 92:
...the descriptive text of a spell description explains whether or not the magic resistance applies, as some spells are not affected by a target’s magic resistance.
The spell Living Link which you reference is found on pg. 51 (for others who might be looking this up). In the description, there is no exception given for magic resistance.
The AD&D Player's Handbook:
Magic resistance is an innate ability--that is, the possessor does not have to do anything special to use it. The creature need not even be aware of the threat for his magic resistance to operate.