I suppose the answer could be 'just because' but given that his father
had a load, including four sons who lived to adulthood and at least
two of his younger brothers had sons, why did Friedrich Wilhelm IV
himself have none ? Or were there some still-born or died in infancy
which simply do not get a mention on royal genealogical websites ? If
not, did he have any bastards ? If none are known, is there a balance
of opinion as to whether it was him or his wife who was infertile ? Or
did they just not get it together often enough ?

wolvies, lol

He was probably sterile.

King Edward VIII of England is believed to have become sterile as a
result of having had measles as a young adult. Apparently although
rare, it can happen if the testicles become infected.

Certainly, the ONLY Kingly Duty is to produce offspring.

Friedrich Wilhelm IV may have had a son, but apparently this is not proven:

http://www.alexanderpalace.org/lostsplendor/iii.html

Friedrich Wilhelm IV as presumed father is also mentioned here:

http://gsteinbe.intrasun.tcnj.edu/royalty/ahnenreihe/Yousoupov.html

By the way, Felix Felixovich (1887-1967), mentioned on the same page,
killed Rasputin.

Thats very interesting. I was just looking into his wife (Elisabeth of
Bavaria) and found that she was a twin - however, her twin sister
Amelie had NINE children... I don't know what that's conclusive off,
except we aren't looking at deficient Bavarian genes. It doesn't prove
whether it was Friedrich Wilhelm or Elisabeth who was the problem...

Thanks :)

Grey Wolf

Two pages on Elisabeth of Bavaria (sorry that they are in German):

http://www.marlesreuth.de/personen_e.html#Elisabeth%20Ludovika%20von%20Bayern

http://www.stadt-bad-kreuznach.de/politik-verwaltung/verwaltung/110-fb/frauenkalender2002/11november.htm

Perhaps a ga-researcher will translate some parts when answering your
question.

FMIV was widely considered mad, although madmen produce children. His
ancestor, Frederick William I was probably psychotic. Another
Hohenzollern, Frederick the Great did not have children either. Some
historians believe he may have been homosexual. Why didn't FM IV have
children? Perhaps he was impotent; perhaps his queen was barren;
perhaps he had a low sperm count; perhaps he was gay, although I doubt
that. Who knows?

I see it mentions childless except that the translation goes bananas

"Die Liebesehe bleibt kinderlos, eine Erklärung dafür könnte die in
den Jugendjahren des Thronfolgers
von Hufeland attestierte Impotenz sein."

turns into

"The dear marriage remains childless, an explanation for it could in
the youth years of the successor to the throne the Impotenz certified
by hoof country be. "

Sadly I can't imagine what 'Impotence certified by hoof country be'
might mean !

Grey Wolf

Using AltaVista to translate
http://www.stadt-bad-kreuznach.de/politik-verwaltung/verwaltung/110-fb/frauenkalender2002/11november.htm
albeit in a rather mangled form, I get the impression that Friedrich
Wilhelm was frequently ill, and that what did for him in 1857-8 was
not a one-off occurrence but just the latest and most severe of these
happenings ? Is that a fair understanding ?

Thanks
Grey Wolf

"hoof country" 
http://www.badlangensalza.de/stadt/htm/net/htdocs/geschichte/hufeland.html

was personal physician (Leibarzt) to Friedrich Wilhelm III since 1801.

"Wilhelm was frequently ill, and that what did for him in 1857-8 was
not a one-off occurrence but just the latest and most severe of these
happenings ? Is that a fair understanding ?"
Yes, this is a fair understanding. However, according to other
websites it was only in 1857 that he became ill.

"Or
did they just not get it together often enough ?"

To cope a little bit with royal privat affairs: 
In the first, very small and intimate 'residence' of the crown prince
Friedrich Wilhelm (IV) an his wife Elisabeth in Charlottenhof/Potsdam
(builded 1826-29), both had no seperate sleeping-rooms. Just one room
with one double bed (no twin bed!). Very unusual in these days. Seems
to be an evidence for the special relationship of this couple, I
guess.

True, having read more of the background of the marriage it is clear
that it was a love-match not a marriage of state etc. They were from
different religions and faced great opposition from both sets of
parents, before finally getting approval for the marriage - which
ceremony was held twice in order to cater to both Protestants and
Catholics. Hence, I find it unlikely that they did not try for a child
- especially as the translation of one of the sites says Elisabeth was
most upset at not having any.

Thus it may lie in her, but quite probably lies in him - despite the
possible bastard (see the Yusopov link)

Grey Wolf