[is there a limit to how many times an item can be reforged? Or does the cost to reforge go up(more mats?)
No, there is not a limit in terms of what you're probably asking.
A reforge costs the following
-Damascus Steel (Amount determined by weapon level and enhancement level).
-An Orange weapon core of the same level
-Two Chunks/Ores that were used to compose the weapon
-An enhancement rune (The unstable one via seal shop works best).
Upon booming your weapon, you then revive it. While in a revived state, it cannot be enhanced further. This is where you must reforge & make the weapon enhanceable again. After that, you try again to plus it. If it fails again, you repeat the process.
There is a failstack system in place that increases the success odds for your next attempt should you fail & consecutive failures create bigger bonuses. These bonuses can go up to 100% success rate so even if you're the unluckiest person in the world, you're eventually guaranteed to succeed. The number of fails needed to reach 100% is proportional to what the weapon's current enhancement level is. Example: A +10 -> +11 can only fail 4 times before hitting 100% success where as +14 -> +15 requires twelve fails to reach 100%.