An IPS just does the same TCP reassembly as the stacks on either end.
Retransmissions aren't a problem. When a hole appears in traffic (because of a lost packet), the IPS forwards the packets after that hole, but also keeps a copy of them. Because it's forwarding those packets, there is no loss in user experience.
When the retransmitted packet fills the whole (completing the puzzle), the IPS then analyzes all those stored packets in order. It combines these into a single stream, so requests split across packets are no problem. If any of those packets trigger a signature, the IPS blocks the retransmitted packet, and kills the TCP connection with RST packets. This caused the target victim to then drop the fragments after the hole that it was buffering.
Thus, packets stream through the IPS with essentially zero latency, but at the same time, TCP is reassembled with no problem.
Over the last decade, hackers have developed methods to attack this system, such as retransmitting TCP segments with different data. Likewise, IPS vendors have developed defense, such as matching their reassembly algorithms with the target system so that it can choose the correct segment to analyze.
Also note that the IPS does full HTTP processing as well. There are likewise ways of corrupting HTTP requests in order to evade the IPS, which IPS vendors defend against.
The upshot is that an IPS introduces only about 100-microseconds (or 0.1 milliseconds) in latency to web requests, while still handling such things as TCP reassembly with no problem.