Hi there,
There are really 2 types of business/network connections:
1) Genuine/deep friendships
2) Mutually beneficial connections
On the first, this should just come naturally! As you work extensively with people, you'll naturally build your relationship. There's no explanation needed here on how to stay friends with someone!
On the second, you essentially need to show your worth. Make it clear that you do a good job in x, y, z. The occasional coffee or check-in (stopping by their desk, shooting a quick message out, etc.) is a good way to keep the connection alive.
If you really want to be methodical, you can “track” contacts on an excel sheet, including when you should reach out to them. I've never done this (prefer to keep it more natural/genuine), but it's one approach!
When you're in town, or in their neck of the woods, reach out and propose a quick catchup.
The key here is pro-activity (without being too needy/pushy as well!)
Wow, this is awesome! Thank you for sharing!