Rather that responding based on gut feelings, I decided to look at some datasheets. Kemet T491 series Tantalum caps are a fairly typical series. 68uF/6V cap has a leakage current of 4.1uA.
When the 555 circuit is nearing the trigger point of 2/3 supply voltage, the voltage drop across the resistor is about 1/3 of the supply voltage. Assuming 5V supply voltage and using your original design with a 0.5M resistor, this results in a voltage of 1.7V, causing 3.4uA to flow through the resistor, which is less than the leakage current of the cap. So I have to admit that
I was wrong about the circuit being unreliable (I admit my mistakes, even highlight them). The circuit will very reliably not work!
You have since revised the circuit to use a 50K resistor and a 720uF cap. Lets see how that does. The resistor current is going to be 10x the original, or 34uA. Assuming we stick with Tantalum caps, a 680uF/6V has a leakage of 40.8uA while two 330uF/6V in parallel have a leakage of 38.6uA.
If we were to look at Aluminum caps, things get even worse. Typical Aluminum caps are about an order of magnitude higher. Specialty caps like United Chemicon KDE or Cornell Dubuilier SXR series are specified as 0.01*C*V which puts a 680uF/6.3V cap at 50uA.
Sooooo as I love to say, there is no free lunch. Your second circuit, the one using 50K caps will overcome the IC's leakage issues, but will succumb to the larger cap's larger internal leakage.
Now if you just had to do it this way, I wold look into "Super Caps" sometimes also called "Gold Caps" They are extremely high capacitance caps (0.1F to 100F). Some varieties are designed for battery backup of SRAM. They have extremely low leakage and extremely high ESR (hundreds of ohms). You may be able to get a 555 circuit to work with those, but the ESR may end up messing up your timing because the ESR may end up being close to the timing resistors. Another thing to worry about is that most are not available in 5.5V ratings.
---55p