This simple cct. uses a diode to peak detect the audio for a DC control bar graph.
For analog Memory you want a Peak detector with decay might do. Putting a suitable Cap after the diode will slow the decay , but also if too big a value will be less sensitive to the peaks due to current drive limits charging the Cap depending on the source.
It is a nice simple bar graph but no simple solution for latching the largest active output other than a priority encoder, a CPLD but not simple.
However if you want to play with a Peak and Hold, you might be able to switch between input and an active peak detector with a clock and analog switch so the active signal and peak signal alternate on the display in some fashion to suit your purpose even tho it is not as you wanted with just the top LED ON.