This is usually in the carrier's end, not the phone (except in one case). If the message exceeds the maximum length, the carrier usually splits the message in several ones, and should deliver them properly (and separately) to your phone.
Other carriers, however, turn these longer messages into MMS, and this is where it might be your phone... If your phone doesn't have the proper configuration (server data, user, password, etc.) for MMS FROM YOUR CARRIER, it won't work. Most carriers can send an SMS to your phone to automatically load all the necessary info, but some require you to pay a visit to a physical store.