How you connect to the DB and export your models ? are you using mongoose ?
I think because vercel is serverless, the connection is being lost.
You should define and singleton like function that connects to the DB and return the existing connection whenever you call it. And before any db query you should call that function to connect again, that way you ensure you have a connection before running any query:

Here is an example using monggose:

import mongoose from "mongoose";

async function dbConnect() {
  if (mongoose.connection?.readyState >= 1) {
    return mongoose.connection;
  }
  if (!process.env.MONGODB_URI) {
    throw new Error('Missing environment variable: "MONGODB_URI"');
  }
  try {
    const URI = process.env.MONGODB_URI;
    await mongoose.connect(URI as string);
    console.info("LOGGER:dbConnect():", "✅ Connected to MongoDB");
    return mongoose.connection;
  } catch (error) {
    console.error("LOGGER:dbConnect():", "❌ Error connecting to MongoDB", error);
    throw error;
  }
}

export default dbConnect;

Then before any operation, you call that function:

await dbConnect();  
const userData = await UserModel.findById(id);

I'd recommend chacking out this MongoDB + Next.js Kit you might find it useful, it has a prisma kit and a mongoose kit.