Pulse SMS imports the latest 250 conversations and up to 500 messages per conversation when you start up the app for the first time. There is no way in the app to increase this limit. It is in place for performance and import time. Nonetheless, conversations can grow as large as you let them after the initial installation.
Additionally, some messages on your phone may be in a format other than SMS/MMS, which Pulse SMS is unable to support at the moment. Such messages cannot be imported into the app. This article about RCS discusses the advanced messaging protocols that some carriers have begun to implement and what they mean for Pulse SMS.