You can increase the log file size limit by the editing the LogSizeInMB value and also make sure to keep the correct log level (3 - normal, 5 - detailed) while replicating the issue. No automatic way of saving logs from the Pulse Client standpoint, however you can write a script to do so. Logs will be appended and will not clear the old entries upon every attempt, rollover will occur i.e. logs gets renamed to .old file after reaching the configured limit.
Log file location - C:\ProgramData\Pulse Secure\Logging\debuglog.log and debuglog.log.old
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