Loose bass can best be described as effecting the pitch of the sound. Imagine if you literally reduced the tension of a bass drum until the skin was no longer tight across the head. The drum would sound loose and lacking the proper pitch.

Describing an amplifier as having loose bass is similar in that the amplifier has a hard time controlling the lower frequencies with quick and sudden bursts of power delivered to the speaker as it is demanded. The result is a loss of proper pitch definition and smearing of the notes surrounding the demand.

This effect can be greatly reduced by not placing too big a demand on the amplifier with speakers that are current hungry and dip below 4 ohms for any length of time. It really is more a matter of mating the amp with the speaker so they are both happy.

An amplifier's damping factor is often eluded to as an indication of its ability to control the speaker cone movement. A higher damping factor usually suggests better control. However, there is more to it than just that. Many tube amplifiers can have excellent bass and awful damping factors.

There are a couple of reasons for loose bass.
Probably the major cause is because of the mass of the cone of the low frequency driver. Low frequencies require lots of air to be moved. That can be done two different ways.
Use a small driver and move it a large distance.
Use a large diameter driver and move it a smaller distance.
The small diameter driver will have a low mass and be able to respond quickly but will have difficulty remaining linear in its travel because of forces applied by its attachment points at extreme travel. Magnet/coil linearity at large travels cause problems also.
Because of these limitations larger cones are normally used.
Larger diameter drivers can move less distance reducing distortion and nonlinearities. But the negative is that the much greater mass of the cone assembly is slower to accellerate and also be more resistent to stopping and reversing direction. Often to the point of overshoot when trying to change direction or speed. This lack of response is loose bass. Driver design and speaker cabinet relationship play a major part in the results.