Abjurant champion: yes
If you had more than one arcane
spellcasting class before becoming an abjurant champion, you
must decide to which class to add each level for the purpose of
determining spells per day, caster level, and spells known.
Abjurant champion’s Spellcasting class feature, quoted in part here, specifically addresses this question: you decide which class to add each level to. Thus, you can make a different choice each time.
In general: usually
Most spellcasting prestige classes use wording similar to abjurant champion, but it’s not a default or assumed rule: each prestige class must specify itself how it works. In fact, there is no default or assumed rule: a prestige class that didn’t say one way or the other would be incomplete, and the DM would have to make a houserule to define it.
Example removed for not actually being a proper example; will try to find another.
For the sake of mentioning it, there is really no reason for a duskblade/wizard to want to advance duskblade spellcasting. Duskblade spellcasting is very weak, and the duskblade’s Arcane Channeling feature applies to all spells, not just duskblade spells. Advancing duskblade spellcasting also does not help you to get Arcane Channeling, since that is a class feature separate from spellcasting. Therefore, a fairly typical path here would be Duskblade 3/Wizard 4/Abjurant Champion 5, progressing wizard with all five wizard levels, so that you can use your 9th-level wizard spellcasting in conjunction with Arcane Channeling.