An IT department exists to satisfy the company's needs, not vice versa. If you can't do the job with the 'resources' given to you, resignation is always an option. But don't fail to do your job and then whine about 'resources'.
Then the users come to IS and piss and whine but get nothing but blank stares in return. And you know, stuff IS does takes time, because we build it to be supportable for the next decade or two (yes really). We write a runbook so someone who's never seen it before can recover it if it fails at 3am, and we make sure it's monitored. We get it signed off by compliance for regulatory oversight. We penetration test it. We back it up offsite and replicate it to the DR site. We stick a generator behind it and we know how many Watts of power it needs (we even know what it weighs so we don't overload the floor in the datacentre). We take its dependencies into account when doing any other work.
Basically, we act like grown-ups with other people's money, something they've largely forgotten in the front office.
People liked and used these apps a lot at my bank too. And that's what made the problem worse. The apps didn't scale, the data was inconsistent or simply not structured (so it was hard to pump it into the main database) and the code was terrible, so it was very hard to add new features.
These things work well for a while (not much data, few users), but when the going gets tough, IT pays the price.