I have tested this, using all your steps, excepting the first one (I added the new instrument track in an existing test project, using HALion Sonic 7 with the 5th Lead preset - HS Factory library). Results below :
I made a render in place two times, the first being with an altered version of the 4th Arp preset of Arpache SX that I saved as _Arp4th_Mod.
The second render has been done immediatly after having relaunched Cubase and opened the project again. The sounds are indeed not the same, as I guess that there is a modulation in the samples used for this HALion Sonic preset, but what is important, if I got your report correctly, is that Arpache SX behaves exactly as previously, both in rhythm and notes duration.
Two more things :
Are you sure that you saved your DIY arpeggio with the Save changes As preset option, in Arpache SX presets dropdown menu ?
After having relaunch Cubase and opened the project again, The Arpache SX window does NOT display the preset used. It’s been one of the pitfalls in Cubase presets management that’s been existing since countless years. But the essential is that the changes made at first are kept from one session to another, at least, on my end :
I noticed also when selecting preset it takes time to load before it starts functioning properly. I mean like not second or two but more like 10 seconds or more.
Have to investigate this more soon as I have time. I see you aren on Windows and I am on mac. Maybe this makes difference?