Why does my solder refuse to stick to pewter?

That beading-up is almost always surface contamination, not heat. You cast this yourself, right? Mold release is the prime suspect. Even a casting that comes out looking clean and silvery can have a micro-thin film of silicone or wax release agent on it, and solder flat-out refuses to wet that stuff. Scraping with a needle file helps but often just smears it around instead of lifting it. Scrub the joint area hard with dish soap and hot water, rinse, then wipe with denatured alcohol or acetone and don't touch it with bare fingers afterward. Skin oil alone will cause the waxed-car effect you're describing.

On flux, the paste from copper pipe work is actually a decent choice here since it's more aggressive than rosin, but it goes stale fast once the jar's been open a while. If yours has been sitting around for years it may be dead. Fresh paste flux or a small bottle of tinner's fluid will both bite into pewter's oxide fine. Rosin on pewter is hit or miss in my expirience.

Your iron isn't the problem either, it's almost too much of a problem in the other direction. Pewter and solder melt at realy close temperatures, and a 40 watt stick parked on a thin tail will slump it before you know it. Tin the wire first, get a little blob of solder frozen on the end, then flux both surfaces, touch the tinned wire to the tail, and feed heat in short touches from the side rather than holding the iron on the joint. You want the solder to flow the instant it gets there and then get the iron off. Honestly though, if the tail section is thin, consider drilling a small hole in the base and pinning the wire into it. You can still wick a bit of solder or epoxy into the joint after, and you've got zero risk of losing the dolphin while you practice.

That pinning idea sounds like the safest bet for me, I once tried gluing a little metal bird onto a wire branch and the glue let go after a few months on the shelf. Cold house in winter probly didn't help but still. Only thing I'm unsure about is the drilling part. I've never drilled into anything that soft before, does the bit kind of grab and pull itself in, or is it like drilling wood? I'd hate to crack the tail trying to make the hole. Also curious how you'd keep the wire from spinning loose in the hole before anything sets.

To answer the drilling worry, pewter is way easier than wood honestly. Soft stuff, the bit just glides through. Only catch is it can grab on the way out the other side if you push hard, so go easy at the end or back it with a scrap of wood. I drilled a couple holes in some soft pewter figurines last year to pin them to a marble base and it took maybe a minute each with a hand drill. Tap the wire in with a dab of epoxy in the hole and that dolphin is never coming off, no heat risk at all.

One thing that saved me on a similar job: regular plumbing solder runs hotter than you want anywhere near soft pewter. I switched to a low-melting electronics style solder for a little figurine repair and suddenly the joint flowed in a second instead of sitting there heating everythign up. Combined with tinning the wire first like was said above, it was basicly foolproof. The short-touch technique matters too, I ruined one piece holding the iron on too long before I figured that out. Cheap swap, might be worth having a spool around for anything cast like this.

One more trick for keeping the tail from slumping while you work: clamp a heat shunt on it. I keep a couple of alligator clips on a steel rod in my box, and on a pewter whale bookend repair last spring I clamped one about a quarter inch up from the joint and it soaked up the heat beautifully. You can even wet a folded rag and rest the tail on it, old jewelers trick.

Also, work on a chunk of scrap wood instead of holding it, pewter conducts heat right into your fingers faster than you expect and a wobbly grip is how tails get snapped off mid-solder.

Curious how you cast it, did you carve a mold yourself or pour into a bought one? That affects what's on the surface.