[RPG] Pathfinder Magus Spellstrike + Spell Combat

No, he can try again with his weapon melee attack. Per spellstrike,

At 2nd level, whenever a magus casts a spell with a range of “touch” from the magus spell list, he can deliver the spell through any weapon he is wielding as part of a melee attack. Instead of the free melee touch attack normally allowed to deliver the spell, a magus can make one free melee attack with his weapon (at his highest base attack bonus) as part of casting this spell. If successful, this melee attack deals its normal damage as well as the effects of the spell. If the magus makes this attack in concert with spell combat, this melee attack takes all the penalties accrued by spell combat melee attacks. This attack uses the weapon’s critical range (20, 19–20, or 18–20 and modified by the keen weapon property or similar effects), but the spell effect only deals ×2 damage on a successful critical hit, while the weapon damage uses its own critical modifier.

There are two separate clauses here - "he can deliver the spell through any weapon he is wielding as part of a melee attack" and "Instead of the free melee touch attack normally allowed to deliver the spell, a magus can make one free melee attack with his weapon." It seems to me that if the attack misses, the charge is held (just like if you were to miss with a touch attack on the same spell, it would be held) and you can try again with your own attacks, just like with normal spell touch attacks. The statement about the freebie doesn't say it's your only chance, in fact it takes pains to make it parallel with the usual free touch attack.

Your GM is correct. Spellstrike doesn't give you a free cast, what it allows you to do is turn your melee touch attack from casting a spell into a normal attack, allowing you to deal your weapon damage in addition to the spell.

At 2nd level, whenever a magus casts a spell with a range of “touch” from the magus spell list, he can deliver the spell through any weapon he is wielding as part of a melee attack. Instead of the free melee touch attack normally allowed to deliver the spell, a magus can make one free melee attack with his weapon (at his highest base attack bonus) as part of casting this spell.

Spellstrike Description on d20pfsrd.

So assuming I've got all my rules straight (someone please double check me on this) you would get a total of 5 melee attacks (4, 4, -1, 4, 4) plus one spell touch affect if at least one of those melee attacks hit. You use spell combat to cast a melee touch attack spell, which spellstrike turns into melee attack at highest BAB. You get your normal attacks, and your attacks from Speed and Sudden Attack. Since missing doesn't cost you your touch attack charge, you can keep trying to deliver your spell with each attack.

As Louis Huppenbauer pointed out, both using the Arcane Pool and Sudden Attack are swift actions, so making 5 melee attacks relies upon you having applied Speed in a previous round (it has a duration of 1 minute).