The US Department of Transport has a general ruling for airlines subject to DOT rules.
The limit of one carry-on bag and one personal bag (e.g., purse or
briefcase) for each traveler does not apply to medical supplies and/or
assistive devices (including service animals and their equipment).
Passengers with disabilities generally may carry medical equipment,
medications, and assistive devices on board the aircraft.
A survey of a random selection of other airlines, shows similar results, although in most cases the airline needs to be notified in advance and have the device approved.
http://www.britishairways.com/en-it/information/travel-assistance/medical-conditions-and-pregnancy
Travelling with medicines or medical equipment
If you need to use your CPAP machine on board you can take it with you
as an additional item to your hand baggage allowance. However if you
don't need to use it on board, it counts towards your hand baggage
allowance. Alternatively, you can check it in at no additional charge.
Just contact PMCU to authorise this as an additional 'checked baggage'
item.
https://www.aa.com/i18n/travelInformation/specialAssistance/mobility-and-medical.jsp
Traveling with mobility and medical devices
A 48-hour notice is required to approve electronic medical devices for
use during a flight All approved medical devices must be battery
operated (battery type will also need to be approved for use inflight)
If you’re bringing an assistive device as a carry-on, it will not
count toward carry-on limits
https://www.airberlin.com/site/affiliate/unternehmen/agb/ABB_en.pdf
The following items of medical equipment may be carried free of charge
as a additional item of baggage (max. weight 23kg), provided that the
passenger registers them in writing well in advance of departure with
the Service Center (by post, email, fax, or, for passengers in
possession of a severe disability pass, by phone) under the contact
details given in section 3.1, and in individual cases a medical
certificate confirming that the equipment is necessary is produced
prior to departure:
- ventilators, asthma equipment, inhalers
- catheters
- materials for dressings (special conditions apply to plaster casts – as per section 6.4.3)
- walking aids (crutches, walking frames)
- sanitary products (nappies), stoma
- shower/WC-seat, transfer board for wheelchair users
- prostheses
- dialysis machines, defibrillators, lymphatic drainage devices, electrotherapy devices
- suction equipment, irrigators
- medicines and injections
- disabled person’s bicycle, therapeutic bicycle, wheelchair bicycle
http://corporate.wizzair.com/en-GB/useful_information/Special_needs
You are allowed to take your CPAP (Continuous Positive Air Pressure
device) device on board subject to providing evidence on the nature of
the equipment. This device can be carried as an additional item. If
you are travelling with such device, please contact our Call Centre at
least 48 hours prior to the scheduled departure of the flight.
https://www.etihadregional.com/en-us/terms-of-use/
In addition to the hand baggage the following items are also allowed:
crutches or other medical equipment provided the passenger has to
depend on them;
http://www.canjet.com/en/home/travel-policies/baggage.aspx
Exceptions may be made for medical equipment required during flight.
If it exceeds the carry-on allowance, please advise your Travel Agent
at time of booking
https://www.ryanair.com/gb/en/useful-info/help-centre/terms-and-conditions
Customers wishing to bring medical equipment as an additional item of
cabin baggage should contact the Ryanair Special Assistance Line to
receive a cabin baggage waiver letter for presentation at the Boarding
Gate.
In general it would appear to be prudent to notify your airline in advance, but I would expect the necessary use of a medical device in-flight would not count towards hand luggage limits.