It could just be a statistics issue. The more you do something the more likely it becomes that you will have a negative outcome. Roll a d20 enough and eventually you will get two nat 1s in a row.
Every time you pierce the septum with the needle, there's a small chance for contamination. There's a chance that some of the pathogens survived the alcohol wipe and will be pushed into the vial. The chance is likely incredibly small. Maybe piercing a multi use vial 4 times is the doctor's personal comfort level, though I couldn't find any information from a quick search that puts a limit on the number of uses beyond following the manufacturers guidelines and expiration date.