In general, this is mostly a firmware/software limitation, not a fundamental hardware one. Multiple community answers note that manufacturers often reserve more advanced bracketing options for higher-end models, even though the camera could often do more.

There are clear examples of cameras in the same family supporting 5 or 7 bracketed frames, and third-party firmware such as Magic Lantern has enabled expanded bracketing on some Canon DSLRs. That strongly suggests the limit is usually not technical in the strict sense.

If your camera only offers 3-shot AEB, there are practical workarounds:

• use external intervalometers that can trigger bracketed sequences
• use remote/software control where supported
• on some cameras, install third-party firmware extensions if available and acceptable to you

Also, not all cameras are limited to 3 frames: some Canon models mentioned in the answers support 2, 3, 5, or 7 bracketed shots. So the real answer is that 3-frame AEB is common by product design, not because cameras are inherently unable to do more.