Generally, if it happens in a person who has had years of chronic illness which probably means they have had multiple IV sites, then their veins are probably sclerosed(hardened...sort of like scarred)from being poked many times. This makes it harder to get IVs in, harder to find a good "spot" to put one. Often, when a person gets into this predicament, they have to have some type of longer term IV access insrted...there are IVs now that can stay in for weeks, and some folks who KNOW they are going to be in for a period of time where they will have multiple IVs (such as a cancer patient starting chemo)will get an IV access port inserted into their chest wall which can just be accessed with one stick each time they need it.
Other folks have thin vein walls, veins that roll, veins that have a lot of valves(which are harder to get through) and any number of other things. IVs are a fairly hard skill to master. Picture putting a needle into a very thin tube(that you can't see since it's under the skin) without having it burst through the other side.