It's been a few days, but if you're still encountering this issue, the issue may be how many mods you're running or the mods are using too much memory.
To fix the former: you'll need to trim down your mods or use FNVEdit to merge the compatible mods.
To fix the latter: download Fallout New Vegas 4 GB.
I had that issue and downloading FNV4GB removed that issue but I was running too many mods so dialogues would randomly pile on top of each other. The soft cap for mods is 140, I believe, but try to keep it below 130.