The correct storage of probiotics is essential for keeping this good and useful bacteria alive. Heat, water and air are the conditions you need to guard against.
In general, all probiotics should be stored in the refridgerator. This is the ideal scenario.
If you can't do that - perhaps you're traveling or simply want to take a bottle of probiotic supplements to work - they can be left at room temperature for several weeks without major loss of viability.
Remember, these are bacteria, so they're fairly hardy sorts of individuals. You don't get to be amongst the oldest life forms on the planet by being too namby pamby!
So long term, fridge is best, but don't obsess about it. Short term, you can tuck a capsule in your handbag and take it 8 hours later at work is fine. You will not have annihilated all the bacteria - despite what some of the manufacturers tell you!
Problems do occur when you start getting much above room temperature. Don't leave them in the hot sun all day.
One other point to be aware of is not to get them wet or damp before you're about to take them. That liquid will bring them out of their "hibernation" and - just like a bear in the spring - they've got to eat. But there is no food within the supplement so they will quickly die.
Probiotics are normally dried and turned into a powder because this keeps them for the longest period of time. As soon as water is added the bacteria return to life and their metabolic processes start up again.
Individually wrapped or single serve capsules or powders will always outlast unprotected capsules although microencapsulated probiotics have that protection "built in".
Don't buy up big quantities just because they're on special. The longer period of time probiotics are stored for, the more viability is lost.
The biggest 3 dangers for the correct storage of probiotics are heat, water and air. Keep them as free as possible from those 3 factors and you will extend their life considerably.