I used to be in Support, and at least in the Lehi office (where most of LEM support lives) the process was the "3 contact close." Support guys are supposed to make at least 3 attempts to contact a customer before closing the ticket, whether by e-mail or phone. Usually these attempts are every other day, so you get 5 business days to respond before Support closes tickets.
In my experience, many customers would go ghost after a day or so, and then wouldn't return calls or e-mails. My thought process was if the issue wasn't important enough to get back to me for a business week, it had either stopped being an issue, resolved itself, or wasn't important. The final message usually includes that you can log into the customer portal and re-open tickets for up to 45 days, so if I closed a ticket today, you'd still have 45 days to respond and say "Hey, it's not fixed and I'm still unhappy!" After 45 days, it's a new ticket. I usually got really good response when I threatened to close the tickets explicitly ie, "I will close this ticket at the end of my shift today if I have not heard back from you." That seemed to light a fire under people, but I had many customers that vanished for 5+ business days and we closed the tickets to get them out of the queues and views so we could focus on customers who were actually responding.
If you're planning on going on vacation and you have an unresolved support ticket, let the support people know and give them an alternative person to work with. If the issue isn't important enough for you to resolve before going to Bermuda for two weeks, it's not important enough for us to keep the ticket open for two weeks. You can re-open the ticket or open a new ticket when you get back from working on your tan.