I haven't focused on goat's milk cheeses really (the odd chevre here and fetta there) so it's not my area of expertise. But I do recall some relevant notes in Ricki Carroll's book Home Cheesemaking. Carroll talks in the introduction about various milks and notes that goat's milk will form a softer curd than cow milk and the curds must be treated gently; in the chapter on goat's milk cheeses she reiterates this. (The one time we made a goat's milk culture backs this up; the yoghurt was far closer to milk than our other cultures). And when she talks about a stretched curd goat's milk cheese (goat's milk provolone) we learn that
The stage of lactation at which goat's milk is produced has a significant effect on whether the curd stretches as it is supposed to. Milk produced early.... makes a curd that stretches beautifully; later.... the curd will stop stretching. Therefore, varying amounts of citric acid are added....
So, generalising here, but: when goat's milk curdles it will usually tend to form a much softer curd than when a cow's milk curdles. And: the quality of the milk will vary greatly depending on where the goat is in its lactation cycle.
Indeed, just checking through my notebook I find that the quality of my chevres has varied a good bit; my latest chevre is great. Previous ones I find notes like 'bit soft' and 'hasn't shrunk away from sides of pot' - possibly because of the dud culture I was using then, though also possibly because goat's milk is a bit more responsive to these changes than cow's milk.
So, solutions: to help the curd harden up a bit, get a bit tougher, maybe add more rennet, as they say above, and/or more culture, and/or a different culture. You could also try giving it a longer time to age and fully separate from the whey. Often the cheese culture appreciates this anyway! And, as others say, maybe it depends on what your goats are eating too - or maybe they're just in a later stage of lactation. Keep on trying and I'm sure you'll get a workable solution!