Assuming his Con is less than 25, and he doesn't have any of the fancy feats etc giving him an extra round or something, then he's probably dead, but most tablew would leave it up to the GM. Our table would allow the Heal to go off and the character would survive. A good GM would probably rule the same way, as the players are the heroes and as such should be on the side that wins.
He would be dead unless his CON is over 48. Damage is usually taken all at once, not a HP at a time.
I disagree that a good GM would let a character survive. If the player was the one who set the condition that is their fault. By the time you have access to Heal and Contingency most characters have a decent amount of HP and setting the threshold that low is a mistake. It should have been set at something like 25% of this HP, not 1 HP. By setting it at 1 HP the player is playing Russian roulette and lost. Cutting a PC a break is one thing, but that is babying them.
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I think this technically comes under the "If complicated or convoluted conditions are prescribed, the whole spell combination (contingency and the companion magic) may fail when triggered." part of the spell. Its not complicated as others have said but its set on such a fine trigger as soon as it happens its too late. I don't think you can set a spell to trigger "if I will take a hit that would drop me to 1 hp or less" as that involves a potential future. GM discretion there I guess, however you didn't have it set up that way to begin with.
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It is not possible to set a trigger of "If the hit will drop me to less than X hit point heal" as that is based on a factor (the damage roll) that is unknown until it is resolved, and when it is resolved it is applied immediately. On the other hand a trigger of "when I am at X hit point or below" is perfectly valid, but it triggers after you have reached that number. As hit points of damage are applied as a sum, you need to survive the damage for Heal to help.
I agree with Mysterious Stranger that keeping the character alive is babying the player. We all know the kind of damage that can be dealt at that level. The player should realize that even selecting 20 hp as the trigger value is cutting a fine line unless the character has a very good constitution.
If you're at the level you failed to avoid death by a contingencied heal spell, suck it up, spend 7k for a diamond and 2k of diamond dust to get rid of your negative levels.
ADVICE
as a GM you should research 'trigger conditions' for PF1, DnD3.5, and Forgotten Realms as they are a bit different. The latter are constrained to 'observable conditions'.
This is a Pathfinder forum, not D&D 3.5.