Mathematica can’t simplify asymptotic expressions containing constant symbols

I want to calculate simple asymptotic expressions involving positive constant symbols ($a > 0$), such as
$$lim_{xtoinfty} operatorname{sech}(a x) sim 2 e^{-a x}$$

Surprisingly, the Asymptotic function of Mathematica can’t calculate this limit.
The code

Assuming(a > 0, Asymptotic(Sech(a x), x -> Infinity))

returns

Sech(a x)

while

Asymptotic(Sech(3 x), x -> Infinity)

correctly returns

2 E^(-3 x)

How can I get Mathematica to evaluate this asymptotic limit correctly?

Edit:

One hack is to replace $a$ with $pi$, then calculate the asymptotic limit, then convert $pi$ back to $a$.

Asymptotic(Sech(a x) /. a -> π, x -> Infinity) /. π -> a

returns the desired limit

2 E^(-a x)