There seems to be a problem with your search feature

There seems to be a problem with your search feature

When I search with in my leads, I find that I often do not pick up some leads when I search under first or last name.   Sometimes I can find those same leads by putting in the last 4 digits of their phone number.   Other times that does not work but the last name will.
 
When I notice these situations, what is puzzling is that fact that what I originally entered to search on, lets say first name, is exactly as I entered in the record and it was in my search. 
 
I am working in a database of about 4000 leads and this has been happening quite often.
 
I would really appreciate this being fixed.
 
Thank you.