Small drill bits must be spun very fast and "pecked" much more frequently than larger bits.
Factor 1 - Cutter surface speed
The surface speed of a drill bit is how fast the cutting edge moves across the material being drilled. This is measured in surface feet per minute (SFM) and is proportional to both the RPM and the diameter of the bit.
When you get down to small sizes, say 1/16", you need high revs to be moving the cutting edge at an appropriate speed, keeping the chip load (and therefore cutting forces) low. The recommended SFM for wood is 600 to 1000.
The recommended drilling speed for a 1/16" bit is on the order of 40,000 RPM:
(SFM * 12) / (Pi * Dia.) = (600 * 12) / (3.14 * 1/16) = 36,688 RPM
which of course is higher than most folks have available. So you'll want to use your fastest speed and feed the bit proportionately more slowly.
Factor 2 - Chip evacuation
Once your hole is more than a couple bit diameters deep, you need to pull the bit out of the hole periodically to clear the chips. Failing to do this causes the bit to bind in the accumulated chips and break the bit. This periodic drill, pull out, drill action is called "pecking".
All the chips formed by a twist drill must be "stored" in the flutes. These can hold at most a few diameters worth of material before they become "packed" with chips. Continuing to drill in this state packs the chips against the wall of the hole and binds the bit, causing it to break.
Pecking is required on small bits at the same number of diameters as a big bit, but since the diameter is small, the pecks need to be what seem like very small amounts, say 1/8" for the 1/16" bit.
By keeping these two things in mind, smaller bits can last as long as larger ones, which for most home users is "indefinitely".