Short answer: Your Togetic's ability will not change upon evolution, there's nothing to worry about.

Long answer (why):

Each individual Pokémon has a "personality value" in its data, at the end of which resides a bit that the game looks at to determine whether that particular Pokémon has its first ability (0) or its second ability (1). Some Pokémon species like Flygon have the same ability listed as both its first and second abilities, so no matter the individual's personality value, it will always have that one ability (Levitate (0) and Levitate (1)). Others, like Togetic, have two: Hustle (0) and Serene Grace (1).

The game checks the "ability bit" in a Pokémon's personality value upon evolution. Trapinch's Hyper Cutter (0) becomes Vibrava's Levitate (0), while Trapinch's Arena Trap (1) becomes Vibrava's Levitate (1).

Likewise, Togetic's Hustle (0) becomes Togekiss's Hustle (0) and Togetic's Serene Grace (1) becomes Togekiss's Serene Grace (1).

However, a Pokémon which normally has the "same" ability between evolutions might change its ability upon evolving if its species gained a new ability in different generation. For example, Porygon and Porygon2 both had Trace (0) and Trace (1) in Gen III. In Gen IV, their species' Trace (1) became Download (1). So, if a Porygon with Trace (1) from Gen III were to evolve into Porygon2 in Gen IV, its ability would change to Download (1).

Togetic and Togekiss's share the exact same abilities consistently throughout the generations, so there's no chance of a change there for ya.