Incremental Backups not Running until Full backup is complete

Hello,

I am new with this BE backup system and need your professional advice.

We do our Full backups every Sunday and our Incremental backups from Monday - Saturday.
Our Full backups takes 3 to 4 days to complete (with verification) and the Incrementals do not
run until then.  So we are losing approximately 3-4 days worth of Incremental backups.

My question is, Is this how BE should work by design?  
What can we do to prevent this Incremental backup data loss?

Thanks in advance.