Generally a first-past the post FPTP electoral system favors a two-party system, aka Duverger's law.
In the UK however, the Lib Dems have managed to survive for (approximately) a century the appearance of Labour, albeit with a substantially reduced electoral/seat share.
Are there any influential theories in political science why the Lib Dems were not eliminated (rendered entirely obsolete) in UK politics?
This is not a duplicate of the UK vs US question. The accepted answer there doesn't even mention the libdems; it talks about the SNP, which is a regional party, and a recent one to boot. Basically that answer is completely sweeping under the rug the libdem issue. Also that question is frankly rather broad; maybe someone will chose to say something about libdems there, maybe not. Actually one answer (the 3rd one by votes right now) does mention the libdems:
The Liberal Democrats have taken their traditional pro-EU center-left position, but now their campaigning is emphasising their EU policy rather than their center-left.
That hardly explains why they survived for 100 years contra to Duverger's law.