When growing any plants it is inevitable that you will experience problems from time to time; snowdrops are no exception.
Most problems can be categorised as either a disease (fungal or viral) or a pest.
Good cultivation practises will go a long way in minimising problems and the effects. Regular feeding of the plants, with a well-balanced plant food will help to maintain vigour. Regular splitting of the clumps enables the bulbs to have the space they need and receive their fair share of water and nutrients from the soil.
Some people will use chemicals in a bid to prevent problems occurring. Whether this is beneficial to the plants I can not comment as I personally do not use any chemical intervention (unless it is in the twin-scaling process). I prefer to deal with a problem if and when it arises usually by discarding the infected plant.