I encounter very short power outages quite often. Typically they last for just couple of seconds - perhaps the power grid maintenance staff just flips the switch to "Off" and then immediately to "On". However this is enough for all kinds of IT equipment to lose power and reboot.
A UPS would help, but it looks like a quite expensive thing - the batteries wear out quickly and the retail price of the unit is considerable.
Are there any other solutions against very short outages?
Your options are:
Basically you'll need batteries somewhere to cover even a couple of seconds of power outage, or a huge spinning slab of something heavy which you can generate energy from in a hurry.
UPSes aren't that expensive, and look even cheaper when you consider the alternatives of losing data or having hardware fail...
And generators aren't any good for such short outages as they take too long to spin-up -- usually you'd have a small UPS to get over the short outages and then a generator for longer ones.
Note that UPS companies (I assume all, but at least APC) give you a dollar amount of hardware which they will cover for replacement if it fails because of power problems whilst connected to a UPS. i.e. Guaranteeing that the power supplied will be spike-free etc.
APC have a table of these amounts on their website. They're obviously pretty certain that it will be fine, as they cover even small UPSes up to many thousands of dollars.
 As mentioned by kmarsh in another answer.
 As mentioned by Evan Anderson in the comments on the question.
Have you and each one of your co-workers complain every time it happens. They might start paying attention to what is going on and fix it.
Flywheels are used in large data centers to cover short power gaps like yours, or to allow time for a backup generator to come on line. They are (typically) only good for 45-60 seconds, and they are expensive, but they have a longer lifetime than UPS batteries, and can make sense for a very large data center.
Another approach was Google's, who integrated a small 12V battery with each rackmount server. The motherboard runs off of 12V input only. This approach works for short, several-second power outages (like yours), for longer outages it only serves to allow a graceful shutdown. It also works if you are large enough to order custom motherboards. :)
Now that we have these unlikely alternatives out of the way...
For most small to medium size data centers, UPS systems make a lot of sense. Start complaining to management now, so when the data loss occurs, you can put your "I told you so" hat on and demand the UPS money, instead of just being on the defensive.
Maybe after significant data loss or even hardware loss, the cost of a UPS wont seem so outrageous.
Are you referring to just a few workstations, servers, or something on a much larger scale?
An additional and diverse feed.
Depending on the load distribution, it may not be more expensive than a UPS unit.
Yet potentially a whole lot more reliable.
From bitter experience I'd prefer the flywheel approach alongside the UPS as I think it has a better chance of working. Don't rely on just one if your data is worth anything.
One nice sunday morning generator testing had been scheduled without anyone with systems in the datacentre being informed (it was one of our own datacentres, but the tech infrastructure people didn't like to share info). Unfortunately they didn't bother checking to see if the UPS was fully functional. The sequence went something like this.
mains -> nothing -> generator -> nothing -> mains
30 racks getting bounced twice in 20 mins, with the survivors of the first power outage getting hit by the second. Fortunately they hadn't decided to try this at our other sites that morning, so at least we kept running.
All you can really do to watch costs is size your UPS solution appropriately. I've seen server rooms with UPS units that sit at 20% usage (or less) because an ambitious salesman got the better of the previous admin.
Hello and thank you for the question,
Today, for short blackout issues, it is possible to use Ultracapacitors.
Ultracapacitors can store a great amount or power very quickly and distribute it also very quickly and reliably, over one million times.