In all my DEI games those 3 factions are at war with a lot of other factions as well. So, maybe a AI thing? As Rome, I've had no problems maintaining allies and Trade Deals as long as I don't get too aggressive. There's a Diplomatic thing, "Expansionism" that turns all factions gradually more hostile the more territory you take for yourself. Also, there were scripted events with Syracuse and then Carthage as Rome expanded into southern Italy and Sicily that resulted in them declaring war on me automatically.