All I can think to ask at the moment is what you mean by 'mixed melee and ranged'. Are they assigned both melee and ranged weapons? That may cause the oddness.
Otherwise, the basic questions are
Do you have different training and combat ammunitions?
Is the ammunition stored in bins?
And how long ago did you assign them to the squad? They seem to like to take their time gathering their gear.
i forget do you have to assign quivers to uniforms? no quivers no place to put ammo
Quivers are assigned automatically if a dwarf is issued a ranged weapon, just as flasks and backpacks are auto-assigned if they are allowed to carry food and drink.
Which reminds me, did you check how many quivers you have? Usually when my marksdorfs don't pick up ammo it's because I forgot to make enough quivers beforehand.
Sadly, I can offer no more help, as for some reason I can never get my ranged dwarves to train properly until my fort is a week from implosion.
There seems to be an oddity, or it may just be my imagination, but when you designate an archery range, even if it encompasses other targets, only the one used to designate the room will be used to train, and the rest will not, unless I designate them all as their own separate rooms.
It's also worth checking that to make sure you've set the direction they are to be shot at and that the right squad is set to train there.