NIPAM (N-isopropylacrylamide)-based polymers in water show many interesting properties in experiments, including a lower critical solution temperature (LCST) at 305 K and a conformational transition of single chains at the same temperature. The results of many simulation studies suggest that standard force fields are able to describe the conformational transition and the phase equilibrium well. We show by performing long molecular dynamics simulations of the direct liquid-liquid phase equilibrium of NIPAM trimers in water that there is no LCST in the expected temperature range for any of the force fields under study. The results show further that the relaxation times of single-chain simulations are considerably longer than anticipated. Conformational transitions of single polymers can therefore not necessarily be used as surrogates for a real phase transition.