Since you asked, my Froggy friend…grammatically, “email’s” technically works in that context:
I haven’t [contacted support] in a LONG time, but when I do [contact support], [email is] my preference
Can be written as you did:
But adding commas will help ensure that someone doesn’t misread the syntax:
I haven’t done this in a LONG time, but when I do, email’s my preference
This is slightly closer to what you intended, but also not exactly:
I haven’t done this in a LONG time but when I do email, it is my preference
Technically you were talking about when you contact support, email is your preference, but the above sentence indicates that when you do email, then email is your preference, which is also not really right.
The lack of commas also leads some people to start to read your sentence in their head as saying:
I haven’t done this in a LONG time, but when I do email is, my preference so
It can cause brain “argggghhhhh-ing”
I also had to go back and re-read the sentence the first time I went through it.
But it wasn’t a big deal. Just made me leave brain skid marks on trying to read your post fast 
Also more clear to say:
I haven’t contacted support in a LONG time, but when I do contact them, email is my preference.
But no biggie for me, you do you, little frog king. As far as I am concerned, if I can understand what is meant by the writer, that’s all that matters to me, personally.