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While reading through the symbol spell I noticed that the spell technically could stay on forever, and during this time the caster could get stronger and thus gain a higher spell save DC.
When rolling against the caster's spell save DC, do you need to roll against their current spell save DC or the one they had while casting the spell?
This is very probably not specifically spelled out in the rules anywhere, but I would argue that it's the one they had when the spell was cast.
It is a permanent (until dispelled) effect, which (to me) means, that after casting it, the caster has no connection to it anymore. Indeed you have to choose all of the specifics (its trigger, effect...) of the spell at the time of casting and your spell slot is consumed at that time as well. Hence, the DC is also fixed at the time of casting, just like everything else.
This is my interpretation of it anyway; as I mentioned, rules don't (as far as I know) address this specifically.
