EASession OutputStream write size limit

Question

I am trying to write to a MFi accessory over the protocol (bluetooth) supported by the accessory from my iOS application using the EASession OutputStream. The issue is that when the written data is more than approximately 3.8Kbytes, the packet is split. For eg. if the packet size to write is 5Kbytes, then the accessory receives the packet in two i.e. first packet of size 3.8Kbytes and second of size 1.2Kbytes. So is there a size limit for writing data over EASession? If so is it configurable so that i can send bigger chunks of data? Thanks, TSJ