I closed the window: is ArkiaSuite closed?
No: closing the window (the X at the top right) keeps ArkiaSuite running, so it can check your mail and ring your reminders.
Step by step
To reopen the window: click the red “A” icon near the clock, at the bottom right of the screen (if you don’t see it, click the little ^ arrow next to the icons).
Right-click this icon: Ouvrir ArkiaSuite (Open ArkiaSuite), Nouveau message (New message), Nouvelle tâche (New task), Rechercher… (Search…).
To really close it: right-click the icon, then Quitter (Quit).