Customer Service only helps with class quests; those cannot be abandoned so you probably abandoned a side quest. In your case, subscribing won't help. Sometimes, you can pick up the quest again at the questgiver; if that doesn't work, you cannot get the quest unfortunately.
I'd still recommend subscribing to get access to the new expansion, you just need to subscribe for one month and will keep access to the chapters released so far even after your subscription expires. Or you can wait until next year when the new chapters come out and grab some bonus rewards: www.swtor.com/fallen-empire/rewards
