Question: Do yeast die after bottling? 

My second batch of beer have been stored in bottles over a month now without producing any co2.
I want to add some priming sugar to start the fermentation again, but I'm unsure if it will help.

Answer: 
Yeast are pretty hardy and it takes time before they completely die off. Even when the nutrients are nearly all consumed the yeast simply go dormant. I have cultured yeast out of beer bottles that were at least a year old. Granted the total viability isn't high but they aren't all dead. Alcohol levels, oxygen levels and storage temp plays a big role.

In your case, adding more priming sugar should work as I am sure there is plenty of yeast around. Be sure the beer is at 70F/21C before starting. You want the beer at room temp as the yeast see the sugar. For ease you may want to try something like Coopers carb tabs. Little pills of sugar for carbing one bottle at a time.
The question has essentially been answered, but I'd like to suggest that you also check out the following rather informative write-up regarding the yeast lifecycle which I've found informative:

<http://www.beer-brewing.com/beer-brewing/brewers_yeast/yeast_life_cycle.htm>