ISP:
TalkTalk

Type of Internet Connection:
DSL

Internet Connection Speed:
12Mb/s

Date & Time:
Multiple. (Last: 26/06/14 10:00 BST)

Frequency:
Always in laggy areas (Mor Dhona, Limsa Lominsa, Labyrinth of the Ancients)

Character Name:
Cuore Sargent

Race:
Hyur F

World:
Excalibur

Class/Level:
Summoner 50

Area and Coordinates:
Limsa Lominsa, Mor Dhona

Party or Solo:
Either

NPC Name:
None

Monster Name:
None

In-Game Time:
No idea.

Steps:
1. Select the "Repair" option whilest on a DoM job
2. The animation for Repairing will eventually show up (but will take a while)
3. After this, unable to perform any actions or use the Aethernet. Furthermore, the Repair itself would not have happened.

While I've not tried it myself, a fellow PS3 player has had the same issue with Converting whilst in Labyrinth of the Ancients.

Model Number of the PlayStation®3 You Are Using
- Model Number: SuperSlim