Are you treating all your tulips exactly the same? Same planting regime, same watering, same compost, same depth in pot? You are, I trust, letting the leaves die back naturally and if in a pot feeding from end of flowering to leaf dieback.

None are in pots Mg. I leave the leaves on, tho' I must admit to not giving them a feed, still some flower beautifully without this & others don't. Some tulip vars, when lifted are all little bulbils rather than the the big bulb that was originally planted.(garlic sometimes does this also).

Unless you buy species tulips, you can't be sure, Feverfew. A lot of the hybrids do exactly what you're describing - produce many bulbils, and those that do often don't flower again. Tulips become naturalized where the conditions suit them best, which is basically very hot summers and cold, not too wet winters, in well drained soil. It's said that the smaller species like T. kaufmannii will last year or year, but that wasn't my experience with those either. Monty Don suggests planting the tulips at least 8 inches deep if you want them to stay in the ground and keep coming, but if you've managed to choose a hybrid that splits into lots of bulbils, it won't make much difference. So to some extent, its luck of the draw, without the advice of a professional tulip grower.

The advice with tulips originally in this country was to lift and store them and replant for the following year, not counting on their flowering much longer than 3 years, but its clear that there are a few which seem quite happy to carry on in the ground. In some cases, it might help to nip off the spent flowers to prevent the bulbs forming seed.

Breaking into smaller bulbs is usually a sign that the bulbs weren't planted deep enough. For perennializing, plant 'em deep. Also, in the warmer parts of the UK, I'd bet that Darwin Hybrids and Multiflora Tulips perennialize better.

I don't know what varieties they are, but I received some tulips bulbs from a friend in Russia more than twenty years ago, and they are still with me, flowering every year (they are in flower now).
Christopher Lloyd used to claim his tulips came back each year, and he gardened on clay.

I have one variety that come back every year and spread but most fizzle out.

You should focus on Kaufmanniana tulips, Greigeii tulips, Fosterania tulips, Darwin Hybrids and species tulips. All the above types flower each year and spread.

You should plant bulbs deeply enough (5" - 6" from base to soil surface). Make sure that the site gets enough sunlight. Growing tulips in shade is no good. You should deadhead the flowers once they finish and then feed the bulbs by forking in some Growmore or blood fish and bone. You can do this before they start flowering

Finally never cut down the leaves while green but allow them to die down naturally after flowering which can take several weeks.

Here's a useful site.

http://www.tulipsinthewoods.com/bulbs/13-ways-to-get-your-tulips-to-come-back/

Thank you everyone for all the excellent feed back. Now I know what to do & which types to have another try with.
Don't think they were planted deeply enough & I also let them do what they wanted to & make seed.

Ah! The energy put into the seeds doesn't go into next year's bloom!

I realised recently that the ones that have survived and spread in our garden are in the poorest driest soil so perhaps like early irises they don't like being moist in summer?

All the Mediterranean bulbs prefer to be baked in summer.