I think Long Distance Relationships work at any distance but you must know that they are naturally temporary; they have a shelf-life (which is a unique time frame based on each unique LDR). So there eventually should be a plan to close the distance at least temporarily to reset the LDR and keep it fresh. A physical meet up is crucial in order to "make it real", else the blossoming relationship can quickly stall and eventually die. Now the frequency of physical meetings will depend on the unique people involved and the distance. Physical touch/affection is very important for people...and (on average) more important for women than for men.
In the mean time, both people must be willing to strengthen their bond, slowly building trust with each other across that distance by making sacrifices, sharing things and opening up or being available (by schedule if necessary), which can be difficult and scary at first because of the dangers (and anonymity) available with today's forms of communication (e.g. catfishing, identity theft, privacy invasion & sharing). Both have to be willing to slowly make themselves vulnerable to the other without having a plan for "if it doesn't work out", because keeping them at an emotional distance eventually will be noticed by the other person the more they try to get to know you.
Then, realize that disagreements will occur...it's a relationship after all. But don't be so quick to block or mute the other person or go silent, at least without specifically telling them how long you need to cool off. Sudden silence can be misinterpreted as ending the relationship or (God forbid) tragedy, which can seriously damage the bond if such a message wasn't originally intended. Like others have said, constant communication is so important, but especially during rough times and lulls.
Also, it's a given that you must be faithful in all relationships, but I think it's especially true in LDRs. Because that person is rarely physically "there" with you, your relationship is primarily a mental and emotional one. Now while most people consider cheating to be primarily a physical act, (as Christ points out in his lesson on Adultery of the heart) emotional cheating is still cheating too. So both must show fidelity to the significant other by ending any emotional affairs you have with other people of interest and well as resisting the temptation of starting any new emotional bonds with the opposite gender (even if the significant other would never know). Both must be committed to each other and only each other. Just because your significant other isn't physically there with you doesn't mean you're not always together in spirit. So to test if you're being faithful to your S.O. ask yourself, "if they were right here with me, would I still do what I'm doing now?"
You know...come to think of it, an LDR may be the perfect example of our current relationship with Christ in spirit (until he comes), so we probably should treat an LDR how we ought to be treating our relationship with Christ.
It can be difficult...but it's not impossible. Just also remember what Christ said in his winepress parable, but for this situation: both people seriously must count the costs of the endeavor before engaging in it.
