You ask this:
Is there any way to achieve what I need or should I look for another hosting solution?
I’m afraid you can’t do that with Amazon EC2 anymore. Here is an excerpt from their page on “Amazon EC2 Instance IP Addressing”; bold emphasis is mind:
You can't manually disassociate the public IP address from your instance after launch. Instead, it's automatically released in certain cases, after which you cannot reuse it. For more information, see Public IP Addresses and External DNS Hostnames. If you require a persistent public IP address that you can associate or disassociate at will, assign an Elastic IP address to the instance after launch instead. For more information, see Elastic IP Addresses.
Which all basically means that the Amazon EC2 pool is ultimately all NAT-ed and all connections are done via DHCP and the only way to get a static—or as they describe it “persistent”—IP address is via their Elastic IP address service.
For more details on Elastic IP addresses and VPC usage, check out this document.