I am always having a broken spoke once in every 500Km I have a Giant Escape hybrid bike, which I bought as a secondhand bicycle. After I had bought it, once in every 500km, according to Strava records, I am always having a broken spoke in rear wheel. Yesterday, I got my sixth broken spoke and I have noticed the old spokes broken always, not the ones I had replaced. 

I asked from a few repair persons but they just replaced the spoke without reasoning. Is there anything I can do to stop this? Because I think this is strange. 





As you can see in this picture most of the broken spokes are on drive side. As I remember I heard sound of breaking when I tried to speed up quickly. 

Most of the time the spokes break at the J Bend, not the nipple/rim.  They all broke in the rear wheel, none in the front wheel.  Most are on the drive side, and few are on the non-drive side.

I am more or less 85kg (187 pounds) who commutes 8km/5miles up and down (16km/10 miles daily) with, most probably, 2kg (4.4 pound/ 4lb7oz) bag. While riding I have to go on concrete roads, uneven terrain, for about 2km/2200 yards. Moreover, I used to ride more than 50km/31 miles on weekends.
Check if all spokes are properly tightened. if some spokes are too loose that can put extra stress on the rest of the spokes which can cause premature failure.
If so (some of the spokes are not properly tensioned) you should true the wheel (or have it done if you don't feel comfortable doing it yourself). 

Is the back wheel the original back wheel that came with the bike or has it been replaced with an aftermarket rear wheel? If so it might be of lesser quality (in which case the spokes will most likely also be of lesser quality). 

How old is the bicycle/how old are the wheels? Metal gets 'tired' after a certain number of load cycles ( https://en.wikipedia.org/wiki/Fatigue_(material) ).
(If the spokes break when trying to tighten them to a normal level the problem is most likely metal fatigue and you should either replace all spokes or replace the wheel (the latter is a more realistic option)). If the wheel is indeed quite old, the spokes are all properly tensioned and there is no other reason to suspect spoke failure metal fatigue might be the issue, if so (as afore mentioned) either replace all (old still remaining) spokes or replace the wheel (which is more conveneint/also cheaper in most cases). Spokes are quite cheap but rebuilding the wheel will take a considerable amount of time.

Where are the spokes failing (at what point on the spoke do they break, near the nipple, near the j-bent?) Can you add an image of the surface of the spoke at the break point? The type of surface at the failure point can give an indication of the failure mode (if it failed due to fatigue or overloading (putting too much stress on the spoke). 

I quote:


  Fatigue usually begins from a stress concentration at the surface. The fatigue cracks grow slowly and usually leaves a striated pattern that looks like a smooth sea shell. Then, when the crack has gone far enough, the object will break suddenly due to the stress in the small remaining area exceeding the ultimate strength. This sudden fracture will usually look different - rough or torn looking. 




Source: http://www.learneasy.info/MDME/MEMmods/MEM30007A/properties/Properties.html



Source: https://www.fastenal.com/en/3289/fastener-fatigue



Source: https://www.sciencedirect.com/topics/engineering/tensiles