Location Location Location!
When picking a location to use your Eye of Ender, there are a number of things you can do to ensure that everything turns out well. While it may feel lower, Eyes of Ender have a 4 in 5 chance of surviving to be used again for whatever purpose. But just because it didn't shatter doesn't mean it can't be destroyed or lost if you're not careful. The two most important things to be mindful of are Cacti and Lava Pools. You should be making sure that you have picked a location that is free of these hazards.
Water can even be a trouble-maker here too. Should an Eye of Ender survive only to plunge into deep water, you may have a significant amount of trouble locating it and if you're outside of your spawn chunks, after 5 minutes it's gone! So avoid using an Eye of Ender in an ocean, or at the very least avoid deep waters.
Avoiding oceans is unfortunate because another quality of a prime location is having a large, flat, open space free from obstructions such as trees or buildings. The reason being is that an Eye of Ender will fly straight through all of these blocks and it may be near impossible for you to decern which direction it went.
Don't Get Cross-Eyed!
Here are some true facts about Strongholds; There are only three of them in the Overworld, they generate roughly between 600 and 1200 blocks from the ORIGIN (X:0,Z:0) of the Overworld and have roughly an equal angle of seperation from each other when measured from the Origin. What this means is that if you are standing at "0,0" and facing a in the direction of a stronghold, the other two are roughly in the direction of a 120° turn to your left and right. Since the Eye of Ender is meant to target the NEAREST stronghold, this means if you are wandering about near the origin of the Overworld and attempting to use an Eye of Ender you may be close to a dividing line between targeting one stronghold over the other an not even know it!
This method REQUIRES that BOTH uses of an Eye of Ender target the same stronghold from two DIFFERENT locations. So to ensure that you don't target two seperate strongholds, here is what you should do: Once you have fired off an Eye of Ender and you believe it has gone off in the direction of an undiscovered stronghold, travel to the left or right of the direction it headed favoring a heading that takes you further from the origin when moving to a secondary location. If the origin is in the opposite direction of the Stronghold, traveling either left or right is fine so long as you also move further from the origin preferrably at a 45° angle.
Don't Move a Muscle!
After you have fired off an Eye of Ender, it is imparative that you remain still and do not move from the exact location that you were in UNTIL you have taken an accurate screenshot. The only movement you should be doing is using your mouse to change which direction you are facing. This method of locating End Portals and Strongholds relies on being able to use the path the Eye of Ender took to create a line that intersects the with the End Portal. YOU are the starting point of that line! If you do a little dance and tumble away from the position you were in when you fired the Eye of Ender, you've all but broken that line.
As the Eye of Ender reaches it's peak position in the air, it will pause there for a moment before shattering or dropping to the ground. To improve your accuracy in locating the End Portal specifically, you will want to be consistantly precise with placing your crosshair at the exact center of the Eye as it floats in the air. This will ensure that you are pointed along the right direction, which may matter more than you think! The farther away the End Portal is, the more sensitive the calculation is to error. Looking just slightly off center of the Eye can create a path that does NOT intersect with the End Portal.
Time is critical while that Eye is in the air. You will want to be able to give yourself all the time you can to aim your crosshair at the Eye once it reaches it's peak location. What will help in this case is anticipating which direction it will head. Assuming you are within 300 blocks from the origin (0,0) it is safe to assume that whichever direction you are from the origin is probably the most likely trajectory the Eye will take. For example, if you were 150 blocks east of the origin and you face East when you throw the Eye of Ender... more than likely the Eye of Ender will take off in a direction in front of you rather than behind you. This will prevent you from frantically spinning around and searching.
This also comes into play when you make your second use of the Eye. Since you already have some idea of what direction a Stronghold is, you should be prepared the second time around and have your crosshair ready at a good first guess position.
Being Wide-Eyed ain't so bad!
Generally speaking you can decrease your margin of error with this calculation by being bold enough to spread out the two locations from which you throw the Eye of Ender. Be cautious with this approach, however, as it increases the possibility of the Eye of Ender targeting a different Stronghold the second time around. You won't want to suddenly cross that invisible threshold and find out that a different Stronghold is closer to your second position.
There IS a behavior of Eyes of Ender that does not appear to be a bug, and depending on what situation you are in could be good OR bad. Imperical data has shown that once you get an Eye of Ender to target a Stronghold it has a tendancy to "stick" with targeting that same Stronghold, even if technically you have moved further away from it than either of the other Strongholds. It is likely you will want to avoid this situation when you have already located 1 or 2 of the Strongholds and the remaining still need(s) to be found. To prevent this from happening as best you can, starting from the Origin run roughly 400 blocks in the opposite direction of any other known Strongholds.
Dont take The Stairs!
Taking ALL of these considerations, tips and suggestions into account... it may be possible that both uses of your Eye of Ender just so happened to target a Spiral Staircase within your nearest stronghold and regretably NOT the End Portal itself. This is a frustrating characteristic of the Eye of Ender's targeting, but a real one. So if you find yourself accurately locating spiral staircases within strongholds, have patience and explore your stronghold. You should be able to find the End Portal quickly enough... assuming it's not detached from the rest of the stronghold... down at layer 5.... buried in lava. Let's just hope you aren't THAT unlucky! ;)