I’m curious why you want to implement one minute log backup/restore process. Is it for DR?
Your log backup frequency shouldn’t impact Delphix performance. Log restore from production to staging was handled entirely at SQL Server level, except for reading backup metadata from MSDB. How fast staging can keep up with production log backups depends on multiple factors...
1. What's the read throughput you are getting from your backup share?
(If you are writing your log backups directly to backup appliances then you are bound to see issues. Backup appliances are tuned for write performance. Read throughput suffers especially when reading multiple files.)
2. Log backups frequently run for more than a minute. In that case, Delphix won’t find the backup entry in MSDB immediately and has to process multiple backups on next iteration. This can add up to restore lags pretty fast.
3. Do you use dedicated staging server? If not, how's the resource utilization on the server looks like?
4. What's the size of your log backup files at different frequency intervals?
Try to quantify the backup share throughput you are getting at different frequencies. Let me know what you find.