NSUrlConnection will automagically keep open and re-use a connection for you, via the HTTP 1.1 protocol. (See this accepted answer). It should do this out of the box, unless you're doing something to modify its default behaviour.
I recommend using a network sniffer to verify that connection re-use is happening (or not), and to verify after what amount of time the connection might be dropped (and hence re-opened on next request). Wireshark is a superb network analyzer with good protocol support.
You could also use a third party library; AFNetworking is nice, well designed, and gets good press. (I used to use ASIHttpRequest but it's recently been retired from active development, and its code structure is more monolithic.)