The most immediately obvious solution is to use Mythic Permanency from Legendary Games' Mythic Magic: Core Spells. (Note that this is 3rd Party, although the link provided does give access to the spell text without purchase of the book - albeit in the most horrendous formatting I've seen in a long time.)
This gets you around, as it states:
A mythic permanency (and any spell it makes permanent) cannot be dispelled by non-mythic means, up to and including non-mythic mage’s disjunction
If mythic magic is out of your purview, then you are pretty much looking at preventing an enemy spellcaster from using (Greater) Dispel Magic on you.
This can be done in many ways, some of the more obvious of which are:
- Having an ally interrupt his spellcasting by threatening his square
- Having an ally counter his (Greater) Dispel Magic cast
- Having an ally cast Silence on the enemy spellcaster will not allow them to cast (Greater)Dispel Magic
- As suggested in other answers, have an ally cast higher CL buff spells with long durations, even if not-necessarily-beneficial effects
The former of these options is of course boosted by having the ally be built for anti-mage combat.
The second can be enhanced by using a Ring of Counterspells, although that would require that the ring be charged with the same Dispel spell as your enemy would be using, and does not work against the area-effect use of Greater Dispel Magic.
The third option will work only when you know that an enemy spellcaster is there, but would be more effective than the first option - presuming they fail their save against the effect. (Unlike being unable to make somatic spell components, being unable to make verbal components without having Silent Spell prevents the use of that spell:
Upon the casting of this spell, complete silence prevails in the affected area. All sound is stopped: Conversation is impossible, spells with verbal components cannot be cast, and no noise whatsoever issues from, enters, or passes through the area.
The fourth option will serve to provide a buffer of spells, so that the (Greater) Dispel Magic has less chance to target your permanencied buffs due to targeting higher CL spells as a priority.
(Note: this does not work if the enemy spellcaster identifies you as having a permanencied buff, and specifically targets that spell.)
Note - you needn't worry about Antimagic Fields, because they simply suppress the effect: leaving the area will restore your permanencied spell to activation.