So you have a bottle of simple syrup, also called sugar syrup, and it has a bottom covered in crystalized sugar. It happens. But must it happen? Or at least, as fast? No.
I was reading through the ingredients in something or other and saw “inverted sugar.” Being a curious sort, I went Googling. What I found was the recipe for inverted sugar. It is very similar to simple syrup. Where sugar has a sweetness rating of 100, simple syrup and inverted sugar have a rating of 130. And the process of making it is very similar. Both break the sugar apart in an effort to keep it in a liquid state, rather than a solid and a liquid. But, inverted sugar should last longer as a liquid than sugar syrup. To read it all, go here. To know the short simple answer, just keep reading.
Your normal simple syrup recipe is one part sugar to one part water, boiled and cooled and bottled.
Inverted sugar is basically, one cup of sugar, one cup of water, a few drops of lemon juice, boiled and then simmered (barely boiling) for 20 minutes, cooled and bottled. The lemon juice acts as a catalyst and will not effect the taste. This process should make your simple syrup, ahem, inverted sugar, not crystalize as quickly, if ever. Same taste, etc.
p.s. You can do a similar thing with honey to make a honey syrup that is far, far easier to mix than normal honey. No need to boil honey syrup, just get it hot in the microwave and stir. Make this stuff in a 50/50 mix. This is the way they do it at the Mai Kai!