diff --git a/pkg/cmd/roachtest/tests/copyfrom.go b/pkg/cmd/roachtest/tests/copyfrom.go
index 04c6df98ed60..5723e2563b4f 100644
--- a/pkg/cmd/roachtest/tests/copyfrom.go
+++ b/pkg/cmd/roachtest/tests/copyfrom.go
@@ -148,16 +148,7 @@ func runCopyFromCRDB(ctx context.Context, t test.Test, c cluster.Cluster, sf int
 	// Enable the verbose logging on relevant files to have better understanding
 	// in case the test fails.
 	startOpts.RoachprodOpts.ExtraArgs = append(startOpts.RoachprodOpts.ExtraArgs, "--vmodule=copy_from=2,insert=2")
-	// The roachtest frequently runs on overloaded instances and can timeout as
-	// a result. We've seen cases where the atomic COPY takes about 2 minutes to
-	// complete, so we set the closed TS and SQL liveness TTL to 5 minutes (to
-	// give enough safety gap, otherwise the closed TS system and lease system
-	// expireation might continuously push the COPY txn not allowing it ever to
-	// complete).
-	clusterSettings := install.MakeClusterSettings(install.ClusterSettingsOption{
-		"kv.closed_timestamp.target_duration": "300s",
-		"server.sqlliveness.ttl":              "300s",
-	})
+	clusterSettings := install.MakeClusterSettings()
 	c.Start(ctx, t.L(), startOpts, clusterSettings, c.All())
 	initTest(ctx, t, c, sf)
 	db, err := c.ConnE(ctx, t.L(), 1)
diff --git a/pkg/sql/colexec/insert.go b/pkg/sql/colexec/insert.go
index 34b055bb7edf..cb16fb2b01ea 100644
--- a/pkg/sql/colexec/insert.go
+++ b/pkg/sql/colexec/insert.go
@@ -190,9 +190,15 @@ func (v *vectorInserter) Next() coldata.Batch {
 			}
 			colexecerror.ExpectedError(err)
 		}
-		log.VEventf(ctx, 2, "copy running batch, autocommit: %v, final: %v, numrows: %d", v.autoCommit, end == b.Length(), end-start)
+		// Similar to tableWriterBase.finalize, we examine whether it's likely
+		// that we'll be able to auto-commit. If it seems unlikely based on the
+		// deadlie, we won't auto-commit which might allow the connExecutor to
+		// get a fresh deadline before committing.
+		autoCommit := v.autoCommit && end == b.Length() &&
+			!v.flowCtx.Txn.DeadlineLikelySufficient()
+		log.VEventf(ctx, 2, "copy running batch, autocommit: %v, numrows: %d", autoCommit, end-start)
 		var err error
-		if v.autoCommit && end == b.Length() {
+		if autoCommit {
 			err = v.flowCtx.Txn.CommitInBatch(ctx, kvba.Batch)
 		} else {
 			err = v.flowCtx.Txn.Run(ctx, kvba.Batch)