Dear Elizabeth
Please don't think you're failing in any way. Thomas was held and cuddled all night until he was 9/ 10 weeks old. He wakes to be fed at 11pm, 2am and 4am, even now at 15 weeks old, and never goes back into his cot after the 4am feed and occassionally has to come into our bed after the 2am feed if he won't settle.
I've got used to the 2am and 4am feeds and am very lucky because my DH takes over from 5am until 7am so I can get a couple of hours uninterupted sleep before the start of each day ( DH doesn't wake at 2am and 4am so normally gets a decent nights sleep so is more than happy to do his bit at 5am - bless him !!! )
Also, during the day Thomas will only sleep if I hold him - so please don't think you're alone there !! I'm much more relaxed about it all now - if Thomas needs to be held then that's fine, like you say, some babies just need to be close to their mums for extra comfort. I tend to tape all my favourite TV programmes in the evenings, go to bed early and then watch my programmes when Thomas is asleep on me the next day.
This phase won't last forever, Thomas has a sleep in the morning and a sleep in the afternoon ( on me ) and feeds around every 3 hours now ( it used to be every hour/ hour and a half just like Zach. ) Some days he'll sit in his bouncy chair or have a kick about on his play mat quite happily and other days he wants more attention, so there I am dancing, singing and making stupid faces/ noises, probably looking like some demented idiot

, to keep him entertained !!
It will get easier - I promise, and in the meantime please know that you're not a failure, you're giving Zach all the love and attention he needs and that will help him grow into a more confident baby in time.
Love
Kim