Sump pumps have limited reach. If the volume of water coming in is higher than the volume the pump can remove from under the home, the pump will run, but leaks and seepage can still happen. This typically seen as seepage in an opposite corner to where the pump is actually installed.
For solving a wet basement, a sump will be needed, however it will need to have it's reach extended by some basic drainage like the GrateDrain in order to be truly effective.
Sump pumps have limited reach by themselvesAs sump pumps remove water from underneath the basement floor, water at higher levels further away fills the void (seeks it's own level) and travels to the low point created by where the pump removes the water. Water further away from the pump could actually be coming into contact with the footing and basement floor, and if the pump can't move the water fast enough, the water touching the floor of the basement could cause seepage or flooding.
Remember water can come in via 3 distinct roots
-the foundation wall (cracks, leaks, and pin holes)
-between the wall and the footing (there's a cold joint where water can sneak through)
-beneath the floor (natural water pooling, water table, springs, saturation, etc)
Sump pumps can most directly deal with the water coming up from the basement floor, but if the cause of water in the basement is from a foundation leak, or water seeping through the cold joint, the sump pump can't isolate and remove it.
This is why sump pumps, alone, can't solve every possible water problem in a basement. Drainage and a possible wall vapor barrier might be needed to solve the issue that you're currently having. Free inspections and estimates are given my most basement waterproofing companies.
Related Reading and Links
Read about the Top 6 Basement Mistakes that contractors and homeowners make. See what other readers have asked in Safe'n'Dry Basement Blog's Reader Questions Section
Ask Jacob A question Directly on Pioneer Basement's Help Forums!