This seems like a pretty big problem on either the part of Bitmex, or the bot creator. There shouldn't be any reason why a VPS shouldn't be able to connect to an API endpoint given it has a valid API key/can authenticate.
I believe it is an issue with a particular endpoint of the API and the fact that the bot doesn't trade every single day... bot owner explained it here:
Note that the negative PNLs of 0.0001 mBTC ( 0.001$ loss) are created by instant 1 contracts trades necessary to escape a bug in the bitmex websocket's position endpoint. After several days without trades, the position value restores and the endpoint returns error when trying to access it. This causes the bots to crash. What's the solution until bitmex fixes the problem? Make instant 1 contract trades to unlock the endpoint. That 0.001$ loss is the fee paid as taker(necessary to close the "unlock trade" in less than 1 second) and the mathematical loss that come from the 0.5$ of spread between the ask and the bid.
I'm unsure as to why BitMEX have not fixed this... or if there is anything else that can be done to work around the problem... in any case, the "losses" from this are ~20 sats per non-trading day... it's not what you would call "huge"... even an entire year of non-trading would only incur around 7300 sats of losses...
If you are running a program on a VPS you have access to, you should be able to review the code to see what triggers the bot to make various trades, and have an idea as to what strategy(ies) it is using. There is no 'guaranteed' way to make money trading, and different strategies will have different success in various trading environments.
You pay for the VPS, but you don't have access to it... that is how the owner is protecting his "IP".