S&H requires charging a capacitor to the voltage being sampled. The capacitor must have extremely low leakage in order to hold the voltage without sagging much. Also, the device reading the voltage must have a very-high (>20megΩ) input resistance (and low bias current) so as not to create an additional sag in the voltage. Maybe you can defer connecting the readout device until you are ready to read out.
It is all about the time-constant (RC), where R is capacitor leakage resistance in parallel with the measurement amplifier input resistance, and C is the capacitance. No sag is impossible. Do the math to see how much sag you can tolerate. 1% in 1sec? 1% in 100sec, etc?
If you really need infinite, then use an A/D and store the digital value.