Is this common?
Not getting a visa to enter the country where a conference is held, is quite common. It is not common for someone to ask for their money back months after a conference though: while people do occasionally get delayed in asking for their money back, usually this is done immediately after finding out that you won't be able to attend the conference. Not months after the conference is over.
I've highlighted two words in what you wrote:
Since conference presentation was mandatory for publication of my paper in the proceedings, I contacted the organizers to let them know about this issue and if there was something I could do like sending a video presentation. I didn't get any response and assumed that they were going to publish it anyways.
If doing X is "mandatory" to get Y, I would recommend not to "assume" you will get Y without doing X. If this happens again in the future, I would perhaps send a polite reminder about my inquiry for presenting the work through video conference (not just one email and then "assume" that the paper will be published even though they never replied to your email), and perhaps make it clear that you would like your money back if there is no way to get the paper published. You might also consider getting a colleague or friend to present the work for you, if you know anyone else going to the conference who you trust with that type of thing (I have had people present my work for me at conferences before, and I've even seen invited speakers gets their post-docs to present their talk for them if they are too busy to attend).
Is there something I could do to get the money back?
You can ask again politely and include a summary of the timeline of events, perhaps with copies underneath of your old email inquiries which were ignored, but I do not recommend to have very high expectations here.
A friend of mine has this motto: "Low expectations, High hopes"