Most likely things to fail are
a) Electrolytic capacitors
b) ceramic (X5R) capacitors.
The lifetime ratings of these is strongly linked to applied voltage and temperature. Without reviewing every part and making replacements on the board, you can't change voltage ratings vs applied (working) voltage. You might be able to have some control over operating temperature.
Estimating lifetime of the rest would require a more intensive design review for voltage deratings on capacitors and power derating on resistors.
In general the best thing you can do is keep temperatures as low as possible -- fans, shade from direct sunlight, don't bury in hot equipment consoles or racks. For example, a decrease of 10C will double the lifetime of an electrolytic capacitor. A similar relationship exists for ceramics in which a modest temperature change results in an exponential increase in lifetime.
Semiconductors are pretty stable as long as they are not operated continuously near their ratings, again, high temperature is bad.
Another thing is to avoid extreme humidity and rapid temperature changes (like don't pull it out of a freezer and mount it over a pot of boiling water).
If you keep everything within 40C, you can expect several years of continuous operation. As a rule of thumb, if you can survive in the environment in which Bela + BBB is mounted, then the electronics will continue to operate several years.
Some things that may degrade before catastrophic failure are things like noise and distortion specs. It's possible these degradations will become audible long before the device completely quits.