While the text of the feat is somewhat ambiguous, there are several indications in the rules that touch spells are not valid targets of Persistent Spell:
If spells with "a fixed range" were intended to include touch spells, why are spells with Personal range called out as allowed? After all, "Range: Personal" is no more variable than "Range: Touch."
The errata for the book in which Persistent Spell was originally printed, Player's Guide to Faerun, explicitly said that touch spells could not be persisted. While subsequent re-publishings of the spell did not include these changes, they're indicative of what the intent of the feat's wording was.
Heroes of Battle p. 113 describes the effect of War Weaver's Enlarge Tapestry class feature:
you cast through an eldritch tapestry have their range category increased: touch spells become close range, close-range spells become medium range, and medium-range spells become long range. Long-range spells and spells with fixed ranges are unaffected.
This rule explicitly draws a distinction between touch spells and spells with fixed ranges, and treats them differently, implying that touch spells are not included in the category of spells with fixed ranges.