As uncomfortable as this may seem, you're going to need to reintroduce yourself. Especially when it comes to informational interviews, you must remember that you are not the only person your contact has met with to conduct an informational interview. In fact, an informational is likely the least memorable meeting a person will have in a given day. So when you’re reaching back out to these contacts after a month or more has passed, you’ll need to help jog their memories a bit. One great way to do this is to reply to the original email chain from when you scheduled the meeting or sent a thank you note (this is the reason that an emailed thank you note is much more important than a handwritten one). If for some reason you have to start a new email chain, you should give the person a little recap of who you are. For example, “I’m the NYU student studying documentary film that you met with last July while I was interning at NBC.” It might sound weird to do this, but it helps the person on the other end by not forcing them to dig back through emails to figure out who you are.
Starting your email this way gives you the opportunity to transition into explaining what you're currently doing. "Since we last met, I've been working as a development assistant at Imagine Entertainment." You can share a tidbit or two about your current position -- something as simple as how much you've learned, or if you think they'll appreciate it, a little nugget about how something they mentioned back when you met helped you. Don't kiss up too much, but if there's something simple and true, it's worth sharing.
Then, you can get to the impetus for your outreach. It's probably best to avoid asking for a favor for yourself after too much time has passed (unless it's particularly timely, like their department is actively hiring for your dream job), but it's within bounds to ask on behalf of someone else -- passing along a friend's resume or trying to set up an informational for a colleague shows you're willing to pay it forward. You can also reach out when there's nothing you need -- just reconnecting for the sake of it, or because you read something interesting about your contact in the news.
The new year is actually the perfect time to renew these connections. There's a good energy in the air to meet up for drinks and re-establish a relationship. And you never know how you may be able to help your contact with their 2019 career goals! That said, this advice does work year-round as well. It's not ideal to lose touch, but life happens, and it's good to know there's a fail safe way to maintain your network when you get too busy.