My headlights, air system, and radio will lose power at times due to low voltage. What could be the cause?

Probably too much unregulated power from the jump box. Get your digital multimeter and test the voltage off car and jump it to the multimeter.

I live in the Great White North (Canada) and a trickle charger and a block heater are essential. I just had my block heater on for 4 days as the temperature was -15'C or - 23' with wind chill. They are only 125 watts.

Ck the fuses here is the info if you already haven't.
1-Headlight washer jets
2-Turn signal flasher
3-Headlight washer, glove box light, engine bay light, instrument cluster
4-License plate lights
5-Instrument cluster, heated seats, auto trans display, outside air temp
6-Central locking system
7-ABS
8-empty
9-heated mirrors
10-empty
11-cruise control(auto trans)
12-on board diagnostic system
13-brake lights
14-interior lights
15-power windows, climate control
16-ABS, anti-slip(?)
17-heated door locks
18-right high beam
19-left high beam
20-right low beam
21-left low beam
22-tail and side marker (right)
23-tail and side marker (left)
24-wipers and washer jets
25-blower for heating/climate control
26-rear window defogger
27-empty
28-fuel pump
29-engine timing
30-sunroof
31-tail lights, cruise control, auto trans
32-engine timing
33-cig lighter
34-engine timing
35-trailer receptacle(?)
36-fog lights
37-radio
38-trunk light, central locking system
39-flashers
40-horn
41-empty
42-empty
43-heated seats

Ok there's the numbers. To figure out what the hell that means you have to look at the inside of the cover to the fuse box. left side of dash panel. Good luck.

1 - Heated washer nozzles, heated outside mirrors 10A
2 - Turn signal system 10A
3 - Illumination 5A
4 - License plate light 5A
5 - Comfort system 7.5A
6 - Central locking system 5A
7 - Back-up lights 10A
8 - Telephone system 5A
9 - ABS 5A
10 - Engine control, gasoline 10A
11 - Instrument cluster, shift lock 5A
12 - B+ (battery positive voltage) for DLC 7.5A
13 - Brake lights 10A
14 - Interior lights, with central locking 10A
- Interior lights, only 5A
15 - Instrument cluster, automatic transmission 5A
16 - A/C-clutch, electrical water pump 10A
17 - Door lock heater 7.5A
18 - Right headlight, high beam 10A
19 - Left headlight, high beam 10A
20 - Right headlight, low beam 15A
21 - Left headlight, low beam 15A
22 - Sidemarker lights, right 5A
23 - Sidemarker lights, left 5A
24 - Wiper system, washer pump 20A
25 - Fresh air blower, air conditioning 25A
26 - Rear window defogger 25A
27 - Daytime running lights 10A
28 - Fuel pump (FP) 15A
29 - Engine control, gasoline 15A
- Engine control, diesel 10A
30 - Sunroof 20A
31 - Automatic transmission 20A
32 - Engine control, injectors, gasoline 10A
- Engine control, injectors, diesel 15A
33 - Headlight washer system 20A
34 - Engine control 10A
35 - Trailer socket 30A
36 - Fog lights 15A
37 - Radio system 10A
38 - Luggage compartment light, central locking system 15A
39 - Emergency flasher system 15A
40 - Dual horn 20A
41 - Cigarette lighter, 12V power outlets 15A
42 - Radio system 25A
43 - Engine control 10A
44 - Heated seats 15A

Have your charging system tested. The battery light is turned on when there is a charging system problem causing an over/under charge condition. You may possibly have an alternator problem. If the battery is not being charged properly, the computer will start shutting down electrical components for protection and to keep enough voltage supply to enable the vehicle to continue running

Probably your charging system (generator)
A Bad battery can cause problems with your charging system also.
Go to your local Auto Parts Store and they will probably check both your charging system and battery for you for Free. They are usually really good about that - they can sell more parts that way.
Let me know what you find out?

check the battery connections are clean and TIGHT as a loose battery connection would cause these symptoms , check the earth for corrosion etc as well

wiper fuse. The wiper motor was, for a very short time, drawing the majority of the power from your system causing the radio to lose its required voltage. The fuse blew to the wipers, ending the power drain, therefore your radio got back the voltage it needed to work. Its kinda like everything goes dead when you start your car, only to come back when you let off the key.

reasons bulbs keep blowning.your head light bulbs is halogen bulbs.dont touch with bare hands.the oils on your hands will make them over heat and blow.so use clean gloves on your hands when replacing the head light bulbs.if all is good.check alternator out put.it could be overcharging causing too much current flow through electrical circuit blowing out bulbs.use a digital volt meter hook it battery with car running battery voltage should be 13.5 to 14.5 volts. if it is 15 to 16 volts too many volts.alternator is faulty.due to lock out features turn off radio before disconnecting battery cables so you wont lose radio playing code.

This is for a 1.8T engine car...
1 - Heated washer nozzle 5A 2 - Turn signal system 10A 3 - Light for glove compartment, air
conditioning, selector lever 5A 4 - License plate light 5A 5 - Instrument cluster, heated seats, cruise control test plug, air conditioning 10A 6 - Control module comfort system 5A 7 - ABS 10A 8 - Automatic headlight beam
adjusting, telephone system 5A 9 - Heated Mirrors 10 - CD changer unit 10A 11 - Cruise control by automatic transmission 5A 12 - B+(battery positive voltage) for on board diagnostic (OBD) 10A 13 - Brake lights 10A 14 - Comfort system 10A 15 - Instrument cluster, automatic transmission 10A 16 - ABS/ASR 10A 17 - Navigation 10A 18 - Right headlight, high beam 10A 19 - Left headlight, high beam 10A 20 - Right headlight, low beam 15A 21 - Left headlight, low beam 15A 22 - Parklight, right 5A 23 - Parklight, left 5A 24 - Wiper system 25A 25 - Fresh air blower, recirculating control air conditioning 30A 26 - Rear window defogger 30A 27 - Rear window wiper system 15A 28 - Fuel pump (FP) 15A 29 - Engine control 20A 30 - Sunroof 20A 31 - Back-up lights, cruise control, automatic transmission 15A 32 - Engine control 20A 33 - Cigarette lighter 15A 34 - Engine control, injectors 15A 35 - Trailer socket 30A 36 - Fog lights 15A 37 - Radio system, telephone system 20A 38 - Comfort system 15A 39 - Emergency flasher system 15A 40 - Dual horn 25A 41 - ABS 25A 42 - free 25A 43 - free 10A 44 - Heated seats 30A