Learn English – Beating them “with the gloves on”

The reference is to the "break-in" process. The word process is left out.

A mechanical system, at times, needs a break-in process because the mechanical properties smoothen themselves into place. A typical example is shoes. Shoes need to be broken-in so that they conform to wearer's feet. Another example is new car engines. Cars should not be driven above a particular speed until their engines are broken in. A third example would be the brakes in a car. With those both "broken-in" and "bed-in" are used.

For the gun break-in process, the reference is in particular to the barrel break-in process, although it also applies to the rest of the gun assembly. The gun break-in is also referred to as "seasoning your gun" or "seasoning your barrel". The process is arduous, requiring the user to fire anywhere from 100 - 500 shots from the gun and cleaning the barrel intermittently, anywhere from every 20 to every 5 rounds fired. Also, the process, if performed incorrectly, can damage the gun.

The gun manufacturers basically do this process on new guns beforehand, so that the gun is ready for normal use.

It is both a time- and cost-saving selling point, thus the advertisement.

As @JohnLawler mentioned in comments, losing steam refers to losing energy.

In other words, energy, or capacity to work can dissipate and be lost.

Because of the disjunction, "or" instead of an "and" conjunction, this concern over the loss of energy may not relate directly to a loss of willpower that allows the subject to resume drinking; instead, it may refer to some other activity, like reliably showing up to work, or something else the narrator might have referred to earlier that was a condition of turning the subject's life around.