I like BytePro's idea of using drugs, too. That's a creative use of something already in the game. Heck, with that idea, you don't really need to house rule it at all--you're just tweaking when death occurs.
The process to bring a sleeper out of cold sleep is typically automatic. Anybody can do it. Just hit the large, square, green switch on the berth. This is a 5+ throw, with a -1 DM if the sleeper had END-6 or less.
The automation probably has a lot to do with the death rate of cold berths.
If you are a Medic-2, then you know enough to operate the berth's manual controls and monitor the unit's operation, adjusting, as needed, the various drugs injected into the patient and adjusting the waking process as the patient comes out of suspended animation. This is where the +1 DM to the throw comes in.
If the throw is failed, then only a Medic-2 or better can attempt revival. He can see the patient going into arrest, and I'm sure that the panel shows red flags all over the place.
No medic means the patient is dead. People are complicated organisms, and a machine can only do so much without a human supervisor. That's why gunners are still needed for ship's weapons.
The Medic-2 gets one chance to save a patient in trouble. He has to override the berth's control unit and hit the functions that will make the berth inject Fast Drug into the patient. This will slow the sleeper's rate of death long enough for the Medic-2 to administer a drug that will heal the patient before he dies.
In game terms, the Fast Drug basically buys the berth character a second roll. Roll 5+ (-1 DM if berther END 6 or less; +1 DM for Medic-2 is automatic) to override the berth's systems and inject the Fast Drug before the character dies. If this roll is failed, the character is dead as the Medic-2 did not act quick enough.
If successful, then the Medic-2 can administer Medical Slow Drug.
Per the Medical Care rules in the combat chapter, the Medical Slow Drug will heal the patient completely in one day, and during that day, the patient will be unconscious/semi-conscious per the Medical Slow Drug rule. After that, the patient will have the effects of the Fast Drug for 60 days--they're basically comatose for two months, per the Fast Drug rule.
If the second throw is made by the Medic-2 to administer the Fast Drug, this results in substantial cost to the patient. Fast Drug costs 200Cr per dose to the ship. Since availability is not always certain, the standard mark up should be at least five times the cost, making it 1,000Cr to the low berther.
Medical Slow Drug costs the ship 100Cr per dose, so this is a 500Cr charge. Together, the low berther, in addition to his 1,000Cr Low Passage, will owe the ship another 1,500Cr should an emergency occur.
The other thing to consider is the legality of the drugs. Many times, low berthers will be brought out of cold sleep once the ship has touched down at its destination. The ship's doctor brings each low berther out of cold sleep, one by one, as the rest of the crew oversee cargo unloading and ship supple refreshment. Most starports have local extrality, but not all. If on a world where the starport does not enjoy extrality, the world could have laws against the use of some of these drugs. Use the Legality rules in the Drugs chapter.
If, indeed, Fast Drug and/or Medical Slow Drug are found to be illegal on a world, this may influence the decision of the Medic-2 to override the low berth's function and attempt to save the patient from dying. It is perfectly legal, by Imperial Law, for a Medic to ignore attempting revival if an incident occurs. (Interpolated by the paragraph describing Low Passage in the rules).