Along with their demo policy, they should provide some kind of guidance on how to follow-up with them. Occasional phone calls are okay, other firms prefer email follow-ups. While in some cases, visiting the label at their offices has worked it is a big risk. In most cases it is best to give them time to contact you first before doing anything too bold. Making sure to follow up is a key to the game, but be sure to do it tastefully.
Once you have some kind of contact with someone on your list, you need to be prepared to work that relationship and expand your contacts within the company. Networking effectively is very important. Yes, you want to stay in touch, but there is a way to do it. Begin to be a presence on their websites and their social media pages, don't take it over, but demonstrate some level of interest in the overall work the company is doing.
Offer congratulations if you notice something positive in the press that they are reporting. Personally acknowledge their press releases as a way of showing you are paying attention to their business. Send updates on your own original submission, and include any new content you may have that stands out.
Stay engaged, put your name in front of them in multiple mediums. “Thoughtful consistency” is a phrase you want to understand and implement into your strategy. If you can do these things, and make music pleasing to the ear, we all will look forward to coming to your concerts and hearing your latest single.