I cannot run Bitcoin-qt during the day because I'm on a tethered 3g connection and do actually need to use most of the available 5-150kbps of bandwidth during the day.
The absolute maximum long term average bandwidth pulling the blockchain can take is about 13.3kbps/sec. I'm not sure what the source of your issues is— it may be due to bandwidth used relaying blocks and transactions to other peers, but you do have enough bandwidth to stay synchronized— at least to within a couple blocks of most current.
That said, for a mobile connection— a thin or lite client is the obvious thing to use. Ideally, you could run one behind a full node that you have absolute trust over (E.g. because you own it), and then you don't even need to worry about the potentially reduced trust model involved.
But it would still be interesting to figure out why your node isn't keeping up.
I frequently forget to load up -qt when I go to sleep, but can't run it during the day because I have other things to do on multiple computers and am too lazy to run back and forth from office to shut -qt off whenever I'm looking for something online. If I used a program like NetLimiter, now having a figure on how much -qt should require to keep blockchain updated, I could probably just limit the amount of bandwidth bitcoin-qt uses, keeping it to maybe 10kbps during the day, unlimited at night, and still stay at or close to current with the blockchain.
If you really need an answer on how I can't keep up.....
At night, -qt is also competing with programs including Skype (which sucks down ~50MB/day), Chrome (usually with auto-updating pages like Gmail because I forget to shut them off), and a miner (consuming 25MB/day more). Chrome varies, but probably consumes roughly 10MB at night. Combined at night, then, assuming 10pm-8am, programs other than -qt consume ~41.25MB over 10 hours, which'd work out to be 4.125MB/h, .06875MB/m, ~9.2kbps. -qt runs only during those 10 hours (when I remember), so for the sake of quick, rough guesstimates, I'll say it has 7.5 hours to run. It was claimed above that blocks are currently ~10% full. I'm not sure how exactly that'd translate to kbps, but I'll just assume it's ~10% of 13.3kbps. So, -qt should then consume only ~1.33kbps. Multiply by 3.2 (24/7.5) and you get 4.256kbps to run -qt from 10pm-8am and keep up with the blockchain. In total, I should be consuming ~13.456kbps at night. But then you have to take service outages into account, which vary widely in times per day, and duration, but it's safe to say my service is out >20% of the time, the ">" being what I'll trade for the bandwidth the miner, Gmail, and Skype won't be utilizing at full capacity. So now the effective rate I need my Internet connection to be at night is ~16.1472kbps. My connection varies wildly, but if I had to take a guess based on MB/day I consume from logs, assuming I'm utilizing the max amount of bandwidth all the time, I have something along the lines of 31kbps on average (almost as fast as dial-up!), a bit under 2x what's required. Though, you could've ignored everything I wrote in this paragraph since you'd only need to read that I start "large" (5MB+) downloads at night. No guarantees on the math, but that should be about where I'm at.
Glad to see such an in-depth discussion. Thanks for everyone's response.