Select query slow in the big table because of expired stats in Microsoft SQL Server
Just looking at the details you have provided, there could be quite some reasons. we can't just predict the exact possible reasons unless you share those select query or queries running slow or you share the execution plans.
Looking at first glance it looked you might have issue with skewed stats. But if you are saying update stats is running daily may be you can try with better sampling rate to see if that helps.
However based on what you are saying that things looked better after manual update stats, this is very much possible that process gets recompiled or bad plan might be getting evicted from cache from that update stats.
My personal experience says you might also been seeing something called parameter sniffing-. There are lot of great articles over the web in case you are experiencing the same.
If you can add more details what is slow with execution plans for pre and post changes can confirm above possibilities.