Unfortunately, the arpeggiator in Ableton doesn’t respond to sustain data.
For Sunday Sounds Ableton Live Song Specific Patches because we’re using Chain Selector for some of these to actually activate/deactivate layers, the midi won’t be passed through until that threshold to activate a given sound is met. So if a note is played at zero for song section, the midi isn’t actually fed through to a sound that isn’t active with chain selector position at zero. There’s ways you could reprogram it to be different, removing the chain selector mapping and replacing it with a really specific volume mapping, for example but generally that ends up being difficult to dial in, which is why we use Chain Selector most of the time.
You'll want to play the note again when you move the Song Section control to a new position.
If you upgrade to Ableton Live Suite, there are some workaround tools.
There are third party arpeggiator plugins online as well that could be used in place of Live’s arpeggiator.
Cthulhu is a good option and only $39.