How do I keep a carry-on bag from being gate-checked when it holds things I cannot be separated from?

The single most effective habit: raise it at check-in, not at the gate.

At the desk there is time, there is a person whose job includes exactly this, and a note can be put on your booking. At the gate there are ninety people behind you and someone trying to close a flight on time. Same request, completely different odds.

What to say is short and specific: that you are carrying medication and medical equipment that must remain with you, and that you would like it noted that the bag is not to be gate-checked. Do not lead with the medical detail, lead with the operational request and give the reason second.

Other things that genuinely help:

• Board early if any mechanism lets you. Many airlines will board passengers with medical needs early on request, and this costs nothing to ask.
• Keep it small. A bag that obviously fits under the seat in front is never taken from you, because the constraint being solved is bin space.
• Carry a doctor's letter describing the equipment. Rarely demanded, occasionally decisive, and it removes any suggestion that you are improvising an excuse.

It helps to know which of the three reasons you are facing, because they have completely different amounts of give.

The bag does not fit. Small regional aircraft have overhead bins that will not physically take a standard carry-on. This is not negotiable at the gate and no amount of explanation changes the dimensions of the bin.

The cabin is full. A full flight runs out of bin space, so the last passengers to board lose. Highly negotiable, it is about sequence, not about you.

A blanket gate-check announcement. Often issued pre-emptively when the crew expects to run out of space. This is the one people assume is absolute and it is usually the most flexible of the three.

For your situation the important thing is that in the second and third cases the crew are solving a space problem and are generally willing to make an exception once they understand yours, but only if they hear about it before they have started collecting bags.

Worth adding: in many places medical equipment and the bag carrying it is treated separately from your carry-on allowance rather than counted within it. That varies by carrier and it is worth checking your specific airline's page before you fly, because it is a much stronger position than asking for a favour.

Going in knowing the airline's own wording turns the conversation from a request into a clarification, and it is noticeably shorter.

One structural point that changes how you should pack regardless of how the conversation goes.

Even with the best preparation, there will be a flight where the aircraft is small and the bag genuinely cannot come aboard. So the goal should not be "this bag never leaves me", it should be "nothing irreplaceable is ever in a bag that could leave me".

In practice that means a second, smaller pouch that is unambiguously personal-item sized and holds the medication itself plus anything you would need in the next day. That pouch never gets checked because it fits under a seat on any aircraft flying. The larger bag can then hold the bulkier equipment and you can afford to lose the argument about it.

Splitting the risk is more reliable than winning every negotiation, and it means the one time you meet an inflexible crew member is not the time it matters.