It depends on the way the frames are made, including the exact steel(s) used [there are many different steels, with widely differing properties, ultimate yield strengths, corrosion resistance, and fatigue limits], the tubing diameters [other things being equal, larger diameters will usually be stiffer and more durable], and the wall thicknesses [very thin-walled steel frames are often not particularly durable].

The same sorts of things can be said for aluminums and various types of aluminum tubing.

Some aluminum frames will far outlast most steel frames.

Some aluminum and steel frames will be about equal in longevity.

Some steel frames will far outlast most aluminum frames.

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"Is an aluminum frame bound to fail at some time of its life?"

There are strong, well built aluminum frames that can easily last a lifetime.

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Rider weight, strength, and riding style have a lot to do with it.

What causes most frames to fail eventually is repeated high stresses.

A 120-pound rider who has a gentle riding style, and rides on smooth roads, can make a frame last for centuries.

A muscular 240-pound hard-riding athletic type who rides aggressively on steep and rough off-road surfaces and high-speed downhills on a regular basis will destroy most frames, steel or aluminum, in short order.