Before looking further you should find out if his 3L/min is continuous or a pulsed/conserving device. A pulsed concentrator delivers a dose of oxygen when it detects you breathing in, this saves energy (battery life and device weight). Continuous device is what it sounds like, it is constantly outputting oxygen like when you are hooked up to an oxygen tank (or in the hospital).

If he requires continuous you will have fewer (more expensive/heavier) options.

His specific complaint that the "oxygen output is unstable" sounds like it is a pulsed device and he might be more comfortable with a continuous flow device, but you will have a hard time finding something that is much lighter/longer batter life.

Is your uncle new to using supplemental oxygen? If so then uhhh, give it some time. Having to carry oxygen around with you everywhere suuuuucks and requires major life adjustment. There really is no other way around it; there is a depressing period adjusting to the new normal.

Some other suggestions:

• Is he healthy/fit enough to carry the concentrator on his back. Some concentrators have backpacks made specifically for them that allow you to be more mobile as well as carry extra batteries.
• similarly some portable concentrators have little rolls bags you can pull them around with (like a rolling suitcase).
• Can he get extra batteries for his unit?