The LDAP Directory Link always Times Out and returns “No Records Found” when the Search Query looks for more than 999 records. Why is this and what can we do to rectify?

By default, there is a maximum return of 1000 records set by Active Directory.

The recommendation is to refine the search criteria so a smaller data set is returned.
For example, instead of searching for "s"

search for  "samuel"

Here' is the explanation from Microsoft: 
To ensure that domain controllers can support service-level guarantees, you can specify operational limits for a number of LDAP operations. These limits prevent specific operations from adversely impacting the performance of the server and also make the server resilient to denial-of-service attacks.