Where are you making this calculation happen?
I went through a similar process when looking at creating a view for activity in the previous quarter.
In the table where 'Days Open' resides, make the field an 'Calculation'. Then, set your calculation as above. With the calculation window, there should be a 'Storage Option' button in the bottom right, in here, check the box for 'Do not Store Calculation Results -- Recalculate when needed'.
This should resolve the issue of the item not updating from day to day.
Be aware that if you are doing any searches or filters based on this filter, it can slow down the results return in larger DB. On the plus side, the Unstored nature helps to make the db that little bit smaller.
To have that calculation auto-updated, the result of that calculation must be unstored.
( see the storage options for that field )