Hi Riva,
Yes I have the two caps, 10 ?f and 0.1 ?f on pin 19 of the 7219 and my LED matrix has Rset resistor value of 28k ohms 2.01 v forward voltage and although there is no reference to the DC forward current in the datasheet (Chinese Ebay matrices) I am settling on a conservative 20 mA.
I have exactly the same circuit built up on veroboard and have no problems with it. As stated this is an intermittent problem where one piece of code will display ok and then if I upload a different code example I then have this problem of it only displaying the first character and then nothing. I have swapped the 7219 for another new one that I have but the problem remains. It certainly is a mystery.