Bluetooth Will Not Pair or Keeps Dropping

They are two different failures with two different fixes.

Pairing is the one-time introduction; connecting is what happens every time afterwards. A device that never appears in the list is a pairing or discovery problem. A device that appears, connects, then drops is a connection problem, and the causes below diverge at that point.

Most pairing failures end here.

Apple guidance starts with checking the accessory instructions, turning the accessory off and on, and confirming it is charged or on power. Many accessories only advertise themselves for a short window after a specific button sequence, and outside that window they are invisible by design even though they are switched on.

A half-remembered pairing blocks a clean one.

When an accessory was connected before, Apple advises unpairing it, putting it back into discovery mode, and pairing again. Do this on the phone or computer as well as on the accessory where it has its own reset. Repeating a failed connection without clearing the old record usually repeats the failure.

Multipoint accessories and device limits cause silent refusals.

Headphones already connected to a laptop often will not accept a phone, and Apple notes that an accessory pairing with some devices but not yours may need unpairing from the others first. Hosts also have limits on simultaneous connections. Disconnect the accessory everywhere else and try once more.

Bluetooth shares 2.4 GHz with Wi-Fi, microwaves, and much else.

Audio that stutters as you move, or only in one room, is congestion or obstruction rather than a fault. Your body between phone and headphones is itself an obstacle at this frequency. Move the source to the same side, reduce the distance, and test away from a busy 2.4 GHz access point; the Wi-Fi bands guide explains why that band is so crowded.