It's a very common problem. Yes, they can be repaired. Usually it means the soldered joint between the charging socket and the motherboard has become fatigued and is making an intermittent connection. Note that this can cause increased resistance and/or sparking and generate a surprising amount of heat, so you risk also damaging the charger and other components on the motherboard. Check if the tip of the charging plug is heating up -- by which I mean too hot to touch, not just warm.
If you're in Dublin, the laptop shop in Dun Laoghaire shopping centre, or their related company in the city centre can fix it. I found them ok (not brilliant) and pricey enough.
Having had this problem with more than one laptop, I will now only buy laptops with a right-angle barrel style power connector, rather than a straight-through one which puts a lot of strain on the charging socket if knocked.