From your description of "a very thin wire" and the fact that it breaks, it is obvious you are using a single strand of solid wire to make the connection to your CR2032 battery holder pin. There are two frequent problems that occur with this practice: tiny nicks in the wire caused by poor wire stripper performance and mechanical fatigue at the wire/solder junction caused by movement of the free end of the wire.
The nick problem is especially difficult to avoid if cheap, opposing "V"-groove, strippers are used. Try using strippers that close to form a precise-diameter round stripping hole. These are available for both solid and stranded wire, so be sure to use one specified for insulated solid wire. If this is 30 AWG insulated wire-wrap wire, it should be stripped using a stripper designed for that purpose. Wire-wrap connections are extremely susceptible to failure from nicks in the wire, which is why the final two or three turns on the wrap post must be made with insulated wire. The insulation provides a form of strain relief. Surprisingly, the single-blade "V"-groove stripper, attached to common and
inexpensive hand wire-wrap/unwrap tools as a flat "spring," works reasonably well. If you are stripping Teflon insulated wire, special wire stripping blades are usually necessary to assure a clean cut through the insulation without penetration of the undelying wire. I often use a new single-edged razor blade, rolling the wire under the blade while carefully controlling the downward pressure. Always inspect stripped solid wire under a magnifying glass for the presence of nicks before using it.
The fatigue problem, usually caused by vibration and movement of the wire after it is soldered, is solved by applying a stiff conformal coating to both the joint and a short length of the insulated portion of the wire extending from the joint. A quick-curing two-part epoxy, or even hot-melt glue, will work for this. Avoid using soft elastomer coatings such as RTV (room-temperature vulcanizing) adhesives.
In an earlier life, I used a viscous red substance called
glyptal varnish. See image below. This was a common substance on the bench of every radio and TV repair shop in the 1950s, often used to solve corona discharge problems in the high-voltage section of TVs and to fix in place the adjustments of tuning coils and potentiometers. It dries to a hard, brittle, consistency.
If you decide to use glyptal varnish, allow plenty of time for the solvents in the varnish to evaporate and the coating to harden before disturbing the solder joint. Purchase only as much as you think you will need in a few months. This stuff slowly hardens in the bottle once opened. You can try to slow the process by wrapping the screw-on cap with electrical tape, but I have had spotty results with that. Hot-melt glue might be a quicker and better alternative. Your mileage (or kilometers) may vary.