Strange Reacurring flat tyre

[Sbudge]

Time to run some cotton wool around the inside of that tyre and see what snags. You might also want to try swapping the old tube with one in the front wheel and see if you get the same effect.

I know it's a daft question but you're not using the same valve cap for example on both of them are you?

 

[Ajax Bay]

If the tube deflates when in situ, you have a puncture (or a valve issue) in both tubes (latter unlikely given change of tube). Likely that cause is the same. You must pump it up well eg to 50mm diameter, and do the sink test. There will be bubbles. That will tell you where (choice of two places relative to valve) the cause is and whether inside (spoke hole/rim tape - file/sand down sharps on side of hole / replace tape with thicker version) or outside (shard embedded - @Sbudge cotton wool test) or maybe on the side (rim as suggested earlier).