A lot of long range mages have very poor mobility and/or escape mechanisms as a penalty in exchange for their spell range. If you notice folks like Cassiopeia, Brand, and Lux, they don't have any effective escapes. This is the main reason why most of them will have to bring Flash as their Summoner's Spell. Ziggs have some sort of escape skill, but it's really hard to use. This is the main reason why gap-closer melee assassins like Diana, Fizz, Akali, Katarina, and Talon can counter long range mages like Lux, Brand, and Ziggs very hard with lots of patience and proper items. Although being said, the melee assassins have terrible farming pontential since they are pushed into their own tower hard by the long range champions in exchange of the ability to kill enemy champions easily (and thus, the long range mage champions are MORE vulnerable to being ganked by junglers for pushing into the enemy melee assassin champion into the enemy tower hard).
Now SHORT-range mages like Annie, Kennen, and Ryze can counter the gap closer melee assassins really well (but they're meant to be built tanky as well as strong AP, so yea).