I would suggest:
Do not connect to IP address with HANA Studio but just use something like "imdbhdb" as host. Of course you need to setup your hosts file before with a line like this:
(C:\Windows\System32\drivers\etc)
54.123.123.234 imdbhdb
Just replace your public IP. This way HANA Studio won't even notice that your instance got a new IP. You need to update the hosts file on each IP change.
By the way: If you won't reuse your elastic IP, it makes no sense to use one...? Just leave the public ip which is associated automatically...